Algebra Examples

$2 x + 3 y = 21$ , $- 6 y = 4 x + 1$

Step 1

Subtract $2 x$ from both sides of the equation.

$3 y = 21 - 2 x$

$- 6 y = 4 x + 1$

Step 2

Divide each term in $3 y = 21 - 2 x$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 y = 21 - 2 x$ by $3$ .

$\frac{3 y}{3} = \frac{21}{3} + \frac{- 2 x}{3}$

$- 6 y = 4 x + 1$

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.

$\frac{3 y}{3} = \frac{21}{3} + \frac{- 2 x}{3}$

$- 6 y = 4 x + 1$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{21}{3} + \frac{- 2 x}{3}$

$- 6 y = 4 x + 1$

$y = \frac{21}{3} + \frac{- 2 x}{3}$

$- 6 y = 4 x + 1$

$y = \frac{21}{3} + \frac{- 2 x}{3}$

$- 6 y = 4 x + 1$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $21$ by $3$ .

$y = 7 + \frac{- 2 x}{3}$

$- 6 y = 4 x + 1$

Step 2.3.1.2

Move the negative in front of the fraction.

$y = 7 - \frac{2 x}{3}$

$- 6 y = 4 x + 1$

$y = 7 - \frac{2 x}{3}$

$- 6 y = 4 x + 1$

$y = 7 - \frac{2 x}{3}$

$- 6 y = 4 x + 1$

$y = 7 - \frac{2 x}{3}$

$- 6 y = 4 x + 1$

Step 3

Divide each term in $- 6 y = 4 x + 1$ by $- 6$ and simplify.

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Step 3.1

Divide each term in $- 6 y = 4 x + 1$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{4 x}{- 6} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{4 x}{- 6} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 x}{- 6} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

$y = \frac{4 x}{- 6} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

$y = \frac{4 x}{- 6} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $4$ and $- 6$ .

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Step 3.3.1.1.1

Factor $2$ out of $4 x$ .

$y = \frac{2 (2 x)}{- 6} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $2$ out of $- 6$ .

$y = \frac{2 (2 x)}{2 (- 3)} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

Step 3.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (2 x)}{2 \cdot - 3} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

Step 3.3.1.1.2.3

Rewrite the expression.

$y = \frac{2 x}{- 3} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

$y = \frac{2 x}{- 3} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

$y = \frac{2 x}{- 3} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

Step 3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{2 x}{3} + \frac{1}{- 6}$

$y = 7 - \frac{2 x}{3}$

Step 3.3.1.3

Move the negative in front of the fraction.

$y = - \frac{2 x}{3} - \frac{1}{6}$

$y = 7 - \frac{2 x}{3}$

$y = - \frac{2 x}{3} - \frac{1}{6}$

$y = 7 - \frac{2 x}{3}$

$y = - \frac{2 x}{3} - \frac{1}{6}$

$y = 7 - \frac{2 x}{3}$

$y = - \frac{2 x}{3} - \frac{1}{6}$

$y = 7 - \frac{2 x}{3}$

Step 4

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

No solution

Step 5