Algebra Examples

$3 x - 2 y = 8$ , $5 x + 3 y + 7$

Step 1

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

$3 x = 8 + 2 y$

Step 2

Divide each term in $3 x = 8 + 2 y$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 x = 8 + 2 y$ by $3$ .

$\frac{3 x}{3} = \frac{8}{3} + \frac{2 y}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{8}{3} + \frac{2 y}{3}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{3} + \frac{2 y}{3}$

Step 3

Replace the variable $x$ with $\frac{8}{3} + \frac{2 y}{3}$ in the expression.

$5 (\frac{8}{3} + \frac{2 y}{3}) + 3 y + 7$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$5 (\frac{8}{3}) + 5 \frac{2 y}{3} + 3 y + 7$

Step 4.2

Multiply $5 (\frac{8}{3})$ .

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Step 4.2.1

Combine $5$ and $\frac{8}{3}$ .

$\frac{5 \cdot 8}{3} + 5 \frac{2 y}{3} + 3 y + 7$

Step 4.2.2

Multiply $5$ by $8$ .

$\frac{40}{3} + 5 \frac{2 y}{3} + 3 y + 7$

Step 4.3

Multiply $5 \frac{2 y}{3}$ .

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Step 4.3.1

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

$\frac{40}{3} + \frac{5 (2 y)}{3} + 3 y + 7$

Step 4.3.2

Multiply $2$ by $5$ .

$\frac{40}{3} + \frac{10 y}{3} + 3 y + 7$

Step 5

To write $7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{10 y}{3} + 3 y + \frac{40}{3} + 7 \cdot \frac{3}{3}$

Step 6

Combine $7$ and $\frac{3}{3}$ .

$\frac{10 y}{3} + 3 y + \frac{40}{3} + \frac{7 \cdot 3}{3}$

Step 7

Combine the numerators over the common denominator.

$\frac{10 y}{3} + 3 y + \frac{40 + 7 \cdot 3}{3}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $7$ by $3$ .

$\frac{10 y}{3} + 3 y + \frac{40 + 21}{3}$

Step 8.2

Add $40$ and $21$ .

$\frac{10 y}{3} + 3 y + \frac{61}{3}$

Step 9

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

$\frac{10 y}{3} + 3 y \cdot \frac{3}{3} + \frac{61}{3}$

Step 10

Combine $3 y$ and $\frac{3}{3}$ .

$\frac{10 y}{3} + \frac{3 y \cdot 3}{3} + \frac{61}{3}$

Step 11

Combine the numerators over the common denominator.

$\frac{10 y + 3 y \cdot 3}{3} + \frac{61}{3}$

Step 12

Combine the numerators over the common denominator.

$\frac{10 y + 3 y \cdot 3 + 61}{3}$

Step 13

Multiply $3$ by $3$ .

$\frac{10 y + 9 y + 61}{3}$

Step 14

Add $10 y$ and $9 y$ .

$\frac{19 y + 61}{3}$