Solve by Graphing -3x-4y=2 , 8y=-6x-4

$- 3 x - 4 y = 2$ , $8 y = - 6 x - 4$

Step 1

Add $3 x$ to both sides of the equation.

$- 4 y = 2 + 3 x$

$8 y = - 6 x - 4$

Step 2

Divide each term in $- 4 y = 2 + 3 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 2 + 3 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{2}{- 4} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{2}{- 4} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

Divide $y$ by $1$ .

$y = \frac{2}{- 4} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

$y = \frac{2}{- 4} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

$y = \frac{2}{- 4} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 4} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$y = \frac{2 \cdot 1}{2 \cdot - 2} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 2} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

Rewrite the expression.

$y = \frac{1}{- 2} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

$y = \frac{1}{- 2} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

$y = \frac{1}{- 2} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{3 x}{- 4}$

$8 y = - 6 x - 4$

Move the negative in front of the fraction.

$y = - \frac{1}{2} - \frac{3 x}{4}$

$8 y = - 6 x - 4$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$8 y = - 6 x - 4$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$8 y = - 6 x - 4$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$8 y = - 6 x - 4$

Step 3

Divide each term in $8 y = - 6 x - 4$ by $8$ and simplify.

Divide each term in $8 y = - 6 x - 4$ by $8$ .

$\frac{8 y}{8} = \frac{- 6 x}{8} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{- 6 x}{8} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Divide $y$ by $1$ .

$y = \frac{- 6 x}{8} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$y = \frac{- 6 x}{8} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$y = \frac{- 6 x}{8} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 6$ and $8$ .

Factor $2$ out of $- 6 x$ .

$y = \frac{2 (- 3 x)}{8} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Cancel the common factors.

Factor $2$ out of $8$ .

$y = \frac{2 (- 3 x)}{2 (4)} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Cancel the common factor.

$y = \frac{2 (- 3 x)}{2 \cdot 4} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Rewrite the expression.

$y = \frac{- 3 x}{4} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$y = \frac{- 3 x}{4} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$y = \frac{- 3 x}{4} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Move the negative in front of the fraction.

$y = - \frac{(3) x}{4} + \frac{- 4}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Cancel the common factor of $- 4$ and $8$ .

Factor $4$ out of $- 4$ .

$y = - \frac{3 x}{4} + \frac{4 (- 1)}{8}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Cancel the common factors.

Factor $4$ out of $8$ .

$y = - \frac{3 x}{4} + \frac{4 \cdot - 1}{4 \cdot 2}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Cancel the common factor.

$y = - \frac{3 x}{4} + \frac{4 \cdot - 1}{4 \cdot 2}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Rewrite the expression.

$y = - \frac{3 x}{4} + \frac{- 1}{2}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$y = - \frac{3 x}{4} + \frac{- 1}{2}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$y = - \frac{3 x}{4} + \frac{- 1}{2}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Move the negative in front of the fraction.

$y = - \frac{3 x}{4} - \frac{1}{2}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$y = - \frac{1}{2} - \frac{3 x}{4}$

Step 4

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

Always true

Step 5

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