Algebra Examples

$5 a + b + c = 11$ $a + 6 b + 3 c = - 1$ $2 a + b - c = - 1$

Step 1

Move all terms not containing $b$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $5 a$ from both sides of the equation.

$b + c = 11 - 5 a$

$a + 6 b + 3 c = - 1$

$2 a + b - c = - 1$

Step 1.2

Subtract $c$ from both sides of the equation.

$b = 11 - 5 a - c$

$a + 6 b + 3 c = - 1$

$2 a + b - c = - 1$

$b = 11 - 5 a - c$

$a + 6 b + 3 c = - 1$

$2 a + b - c = - 1$

Step 2

Replace all occurrences of $b$ with $11 - 5 a - c$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $b$ in $a + 6 b + 3 c = - 1$ with $11 - 5 a - c$ .

$a + 6 (11 - 5 a - c) + 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $a + 6 (11 - 5 a - c) + 3 c$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$a + 6 \cdot 11 + 6 (- 5 a) + 6 (- c) + 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

Step 2.2.1.1.2

Simplify.

Tap for more steps...

Step 2.2.1.1.2.1

Multiply $6$ by $11$ .

$a + 66 + 6 (- 5 a) + 6 (- c) + 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

Step 2.2.1.1.2.2

Multiply $- 5$ by $6$ .

$a + 66 - 30 a + 6 (- c) + 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

Step 2.2.1.1.2.3

Multiply $- 1$ by $6$ .

$a + 66 - 30 a - 6 c + 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

$a + 66 - 30 a - 6 c + 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

$a + 66 - 30 a - 6 c + 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

Step 2.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1.2.1

Subtract $30 a$ from $a$ .

$- 29 a + 66 - 6 c + 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

Step 2.2.1.2.2

Add $- 6 c$ and $3 c$ .

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$2 a + b - c = - 1$

Step 2.3

Replace all occurrences of $b$ in $2 a + b - c = - 1$ with $11 - 5 a - c$ .

$2 a + 11 - 5 a - c - c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $2 a + 11 - 5 a - c - c$ .

Tap for more steps...

Step 2.4.1.1

Remove parentheses.

$2 a + 11 - 5 a - c - c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 2.4.1.2

Subtract $5 a$ from $2 a$ .

$- 3 a + 11 - c - c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 2.4.1.3

Subtract $c$ from $- c$ .

$- 3 a + 11 - 2 c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$- 3 a + 11 - 2 c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$- 3 a + 11 - 2 c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$- 3 a + 11 - 2 c = - 1$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 3

Solve for $a$ in $- 3 a + 11 - 2 c = - 1$ .

Tap for more steps...

Step 3.1

Move all terms not containing $a$ to the right side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $11$ from both sides of the equation.

$- 3 a - 2 c = - 1 - 11$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 3.1.2

Add $2 c$ to both sides of the equation.

$- 3 a = - 1 - 11 + 2 c$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 3.1.3

Subtract $11$ from $- 1$ .

$- 3 a = - 12 + 2 c$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$- 3 a = - 12 + 2 c$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 3.2

Divide each term in $- 3 a = - 12 + 2 c$ by $- 3$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 3 a = - 12 + 2 c$ by $- 3$ .

$\frac{- 3 a}{- 3} = \frac{- 12}{- 3} + \frac{2 c}{- 3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 3 a}{- 3} = \frac{- 12}{- 3} + \frac{2 c}{- 3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 3.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 12}{- 3} + \frac{2 c}{- 3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$a = \frac{- 12}{- 3} + \frac{2 c}{- 3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$a = \frac{- 12}{- 3} + \frac{2 c}{- 3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Simplify each term.

Tap for more steps...

Step 3.2.3.1.1

Divide $- 12$ by $- 3$ .

$a = 4 + \frac{2 c}{- 3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 3.2.3.1.2

Move the negative in front of the fraction.

$a = 4 - \frac{2 c}{3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$a = 4 - \frac{2 c}{3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$a = 4 - \frac{2 c}{3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$a = 4 - \frac{2 c}{3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

$a = 4 - \frac{2 c}{3}$

$- 29 a + 66 - 3 c = - 1$

$b = 11 - 5 a - c$

Step 4

Replace all occurrences of $a$ with $4 - \frac{2 c}{3}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $a$ in $- 29 a + 66 - 3 c = - 1$ with $4 - \frac{2 c}{3}$ .

$- 29 (4 - \frac{2 c}{3}) + 66 - 3 c = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Simplify $- 29 (4 - \frac{2 c}{3}) + 66 - 3 c$ .

Tap for more steps...

Step 4.2.1.1

Simplify each term.

Tap for more steps...

Step 4.2.1.1.1

Apply the distributive property.

$- 29 \cdot 4 - 29 (- \frac{2 c}{3}) + 66 - 3 c = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.1.2

Multiply $- 29$ by $4$ .

$- 116 - 29 (- \frac{2 c}{3}) + 66 - 3 c = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.1.3

Multiply $- 29 (- \frac{2 c}{3})$ .

Tap for more steps...

Step 4.2.1.1.3.1

Multiply $- 1$ by $- 29$ .

$- 116 + 29 (\frac{2 c}{3}) + 66 - 3 c = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.1.3.2

Combine $29$ and $\frac{2 c}{3}$ .

$- 116 + \frac{29 (2 c)}{3} + 66 - 3 c = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.1.3.3

Multiply $2$ by $29$ .

$- 116 + \frac{58 c}{3} + 66 - 3 c = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

$- 116 + \frac{58 c}{3} + 66 - 3 c = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

$- 116 + \frac{58 c}{3} + 66 - 3 c = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.2

Add $- 116$ and $66$ .

$\frac{58 c}{3} - 50 - 3 c = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.3

To write $- 3 c$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{58 c}{3} - 3 c \cdot \frac{3}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.4

Simplify terms.

Tap for more steps...

Step 4.2.1.4.1

Combine $- 3 c$ and $\frac{3}{3}$ .

$\frac{58 c}{3} + \frac{- 3 c \cdot 3}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.4.2

Combine the numerators over the common denominator.

$\frac{58 c - 3 c \cdot 3}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

$\frac{58 c - 3 c \cdot 3}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.5

Simplify each term.

Tap for more steps...

Step 4.2.1.5.1

Simplify the numerator.

Tap for more steps...

Step 4.2.1.5.1.1

Factor $c$ out of $58 c - 3 c \cdot 3$ .

Tap for more steps...

Step 4.2.1.5.1.1.1

Factor $c$ out of $58 c$ .

$\frac{c \cdot 58 - 3 c \cdot 3}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.5.1.1.2

Factor $c$ out of $- 3 c \cdot 3$ .

$\frac{c \cdot 58 + c (- 3 \cdot 3)}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.5.1.1.3

Factor $c$ out of $c \cdot 58 + c (- 3 \cdot 3)$ .

$\frac{c (58 - 3 \cdot 3)}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

$\frac{c (58 - 3 \cdot 3)}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.5.1.2

Multiply $- 3$ by $3$ .

$\frac{c (58 - 9)}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.5.1.3

Subtract $9$ from $58$ .

$\frac{c \cdot 49}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

$\frac{c \cdot 49}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.2.1.5.2

Move $49$ to the left of $c$ .

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 5 a - c$

Step 4.3

Replace all occurrences of $a$ in $b = 11 - 5 a - c$ with $4 - \frac{2 c}{3}$ .

$b = 11 - 5 (4 - \frac{2 c}{3}) - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4

Simplify the right side.

Tap for more steps...

Step 4.4.1

Simplify $11 - 5 (4 - \frac{2 c}{3}) - c$ .

Tap for more steps...

Step 4.4.1.1

Simplify each term.

Tap for more steps...

Step 4.4.1.1.1

Apply the distributive property.

$b = 11 - 5 \cdot 4 - 5 (- \frac{2 c}{3}) - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.1.2

Multiply $- 5$ by $4$ .

$b = 11 - 20 - 5 (- \frac{2 c}{3}) - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.1.3

Multiply $- 5 (- \frac{2 c}{3})$ .

Tap for more steps...

Step 4.4.1.1.3.1

Multiply $- 1$ by $- 5$ .

$b = 11 - 20 + 5 (\frac{2 c}{3}) - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.1.3.2

Combine $5$ and $\frac{2 c}{3}$ .

$b = 11 - 20 + \frac{5 (2 c)}{3} - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.1.3.3

Multiply $2$ by $5$ .

$b = 11 - 20 + \frac{10 c}{3} - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 20 + \frac{10 c}{3} - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = 11 - 20 + \frac{10 c}{3} - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.2

Subtract $20$ from $11$ .

$b = - 9 + \frac{10 c}{3} - c$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.3

To write $- c$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = - 9 + \frac{10 c}{3} - c \cdot \frac{3}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.4

Simplify terms.

Tap for more steps...

Step 4.4.1.4.1

Combine $- c$ and $\frac{3}{3}$ .

$b = - 9 + \frac{10 c}{3} + \frac{- c \cdot 3}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.4.2

Combine the numerators over the common denominator.

$b = - 9 + \frac{10 c - c \cdot 3}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = - 9 + \frac{10 c - c \cdot 3}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.5

Simplify each term.

Tap for more steps...

Step 4.4.1.5.1

Simplify the numerator.

Tap for more steps...

Step 4.4.1.5.1.1

Factor $c$ out of $10 c - c \cdot 3$ .

Tap for more steps...

Step 4.4.1.5.1.1.1

Factor $c$ out of $10 c$ .

$b = - 9 + \frac{c \cdot 10 - c \cdot 3}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.5.1.1.2

Factor $c$ out of $- c \cdot 3$ .

$b = - 9 + \frac{c \cdot 10 + c (- 1 \cdot 3)}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.5.1.1.3

Factor $c$ out of $c \cdot 10 + c (- 1 \cdot 3)$ .

$b = - 9 + \frac{c (10 - 1 \cdot 3)}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = - 9 + \frac{c (10 - 1 \cdot 3)}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.5.1.2

Multiply $- 1$ by $3$ .

$b = - 9 + \frac{c (10 - 3)}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.5.1.3

Subtract $3$ from $10$ .

$b = - 9 + \frac{c \cdot 7}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = - 9 + \frac{c \cdot 7}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 4.4.1.5.2

Move $7$ to the left of $c$ .

$b = - 9 + \frac{7 c}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = - 9 + \frac{7 c}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = - 9 + \frac{7 c}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = - 9 + \frac{7 c}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

$b = - 9 + \frac{7 c}{3}$

$\frac{49 c}{3} - 50 = - 1$

$a = 4 - \frac{2 c}{3}$

Step 5

Solve for $c$ in $\frac{49 c}{3} - 50 = - 1$ .

Tap for more steps...

Step 5.1

Move all terms not containing $c$ to the right side of the equation.

Tap for more steps...

Step 5.1.1

Add $50$ to both sides of the equation.

$\frac{49 c}{3} = - 1 + 50$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 5.1.2

Add $- 1$ and $50$ .

$\frac{49 c}{3} = 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

$\frac{49 c}{3} = 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 5.2

Multiply both sides of the equation by $\frac{3}{49}$ .

$\frac{3}{49} \cdot \frac{49 c}{3} = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 5.3

Simplify both sides of the equation.

Tap for more steps...

Step 5.3.1

Simplify the left side.

Tap for more steps...

Step 5.3.1.1

Simplify $\frac{3}{49} \cdot \frac{49 c}{3}$ .

Tap for more steps...

Step 5.3.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.3.1.1.1.1

Cancel the common factor.

$\frac{3}{49} \cdot \frac{49 c}{3} = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 5.3.1.1.1.2

Rewrite the expression.

$\frac{1}{49} \cdot (49 c) = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

$\frac{1}{49} \cdot (49 c) = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 5.3.1.1.2

Cancel the common factor of $49$ .

Tap for more steps...

Step 5.3.1.1.2.1

Factor $49$ out of $49 c$ .

$\frac{1}{49} \cdot (49 (c)) = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 5.3.1.1.2.2

Cancel the common factor.

$\frac{1}{49} \cdot (49 c) = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 5.3.1.1.2.3

Rewrite the expression.

$c = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

$c = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

$c = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

$c = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 5.3.2

Simplify the right side.

Tap for more steps...

Step 5.3.2.1

Cancel the common factor of $49$ .

Tap for more steps...

Step 5.3.2.1.1

Cancel the common factor.

$c = \frac{3}{49} \cdot 49$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 5.3.2.1.2

Rewrite the expression.

$c = 3$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

$c = 3$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

$c = 3$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

$c = 3$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

$c = 3$

$b = - 9 + \frac{7 c}{3}$

$a = 4 - \frac{2 c}{3}$

Step 6

Replace all occurrences of $c$ with $3$ in each equation.

Tap for more steps...

Step 6.1

Replace all occurrences of $c$ in $b = - 9 + \frac{7 c}{3}$ with $3$ .

$b = - 9 + \frac{7 (3)}{3}$

$c = 3$

$a = 4 - \frac{2 c}{3}$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $- 9 + \frac{7 (3)}{3}$ .

Tap for more steps...

Step 6.2.1.1

Multiply $7$ by $3$ .

$b = - 9 + \frac{21}{3}$

$c = 3$

$a = 4 - \frac{2 c}{3}$

Step 6.2.1.2

Divide $21$ by $3$ .

$b = - 9 + 7$

$c = 3$

$a = 4 - \frac{2 c}{3}$

Step 6.2.1.3

Add $- 9$ and $7$ .

$b = - 2$

$c = 3$

$a = 4 - \frac{2 c}{3}$

$b = - 2$

$c = 3$

$a = 4 - \frac{2 c}{3}$

$b = - 2$

$c = 3$

$a = 4 - \frac{2 c}{3}$

Step 6.3

Replace all occurrences of $c$ in $a = 4 - \frac{2 c}{3}$ with $3$ .

$a = 4 - \frac{2 (3)}{3}$

$b = - 2$

$c = 3$

Step 6.4

Simplify the right side.

Tap for more steps...

Step 6.4.1

Simplify $4 - \frac{2 (3)}{3}$ .

Tap for more steps...

Step 6.4.1.1

Simplify each term.

Tap for more steps...

Step 6.4.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.4.1.1.1.1

Cancel the common factor.

$a = 4 - \frac{2 \cdot 3}{3}$

$b = - 2$

$c = 3$

Step 6.4.1.1.1.2

Divide $2$ by $1$ .

$a = 4 - 1 \cdot 2$

$b = - 2$

$c = 3$

$a = 4 - 1 \cdot 2$

$b = - 2$

$c = 3$

Step 6.4.1.1.2

Multiply $- 1$ by $2$ .

$a = 4 - 2$

$b = - 2$

$c = 3$

$a = 4 - 2$

$b = - 2$

$c = 3$

Step 6.4.1.2

Subtract $2$ from $4$ .

$a = 2$

$b = - 2$

$c = 3$

$a = 2$

$b = - 2$

$c = 3$

$a = 2$

$b = - 2$

$c = 3$

$a = 2$

$b = - 2$

$c = 3$

Step 7

List all of the solutions.

$a = 2, b = - 2, c = 3$