Solve by Graphing 3x-2y=8 , 6x-4y=20

$3 x - 2 y = 8$ , $6 x - 4 y = 20$

Step 1

Subtract $3 x$ from both sides of the equation.

$- 2 y = 8 - 3 x$

$6 x - 4 y = 20$

Step 2

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

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

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

$6 x - 4 y = 20$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$6 x - 4 y = 20$

Divide $y$ by $1$ .

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

$6 x - 4 y = 20$

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

$6 x - 4 y = 20$

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

$6 x - 4 y = 20$

Simplify the right side.

Simplify each term.

Divide $8$ by $- 2$ .

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

$6 x - 4 y = 20$

Dividing two negative values results in a positive value.

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

$6 x - 4 y = 20$

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

$6 x - 4 y = 20$

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

$6 x - 4 y = 20$

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

$6 x - 4 y = 20$

Step 3

Subtract $6 x$ from both sides of the equation.

$- 4 y = 20 - 6 x$

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

Step 4

Divide each term in $- 4 y = 20 - 6 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 20 - 6 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{20}{- 4} + \frac{- 6 x}{- 4}$

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{20}{- 4} + \frac{- 6 x}{- 4}$

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

Divide $y$ by $1$ .

$y = \frac{20}{- 4} + \frac{- 6 x}{- 4}$

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

$y = \frac{20}{- 4} + \frac{- 6 x}{- 4}$

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

$y = \frac{20}{- 4} + \frac{- 6 x}{- 4}$

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

Simplify the right side.

Simplify each term.

Divide $20$ by $- 4$ .

$y = - 5 + \frac{- 6 x}{- 4}$

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

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

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

$y = - 5 + \frac{- 2 (3 x)}{- 4}$

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

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$y = - 5 + \frac{- 2 (3 x)}{- 2 \cdot 2}$

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

Cancel the common factor.

$y = - 5 + \frac{- 2 (3 x)}{- 2 \cdot 2}$

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

Rewrite the expression.

$y = - 5 + \frac{3 x}{2}$

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

$y = - 5 + \frac{3 x}{2}$

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

$y = - 5 + \frac{3 x}{2}$

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

$y = - 5 + \frac{3 x}{2}$

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

$y = - 5 + \frac{3 x}{2}$

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

$y = - 5 + \frac{3 x}{2}$

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

Step 5

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

No solution

Step 6

Solve by Graphing 3x-2y=8 , 6x-4y=20

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