Solve by Graphing 3x+2y=4 2x-y=5

$3 x + 2 y = 4$ $2 x - y = 5$

Step 1

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

$2 y = 4 - 3 x$

$2 x - y = 5$

Step 2

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

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

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

$2 x - y = 5$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$2 x - y = 5$

Divide $y$ by $1$ .

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

$2 x - y = 5$

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

$2 x - y = 5$

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

$2 x - y = 5$

Simplify the right side.

Simplify each term.

Divide $4$ by $2$ .

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

$2 x - y = 5$

Move the negative in front of the fraction.

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

$2 x - y = 5$

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

$2 x - y = 5$

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

$2 x - y = 5$

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

$2 x - y = 5$

Step 3

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

$- y = 5 - 2 x$

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

Step 4

Divide each term in $- y = 5 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y = 5 - 2 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{5}{- 1} + \frac{- 2 x}{- 1}$

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

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{5}{- 1} + \frac{- 2 x}{- 1}$

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

Divide $y$ by $1$ .

$y = \frac{5}{- 1} + \frac{- 2 x}{- 1}$

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

$y = \frac{5}{- 1} + \frac{- 2 x}{- 1}$

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

Simplify the right side.

Simplify each term.

Divide $5$ by $- 1$ .

$y = - 5 + \frac{- 2 x}{- 1}$

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

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y = - 5 - 1 \cdot (- 2 x)$

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

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y = - 5 - (- 2 x)$

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

Multiply $- 2$ by $- 1$ .

$y = - 5 + 2 x$

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

$y = - 5 + 2 x$

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

$y = - 5 + 2 x$

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

$y = - 5 + 2 x$

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

Step 5

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

$(2, - 1)$

Step 6

Solve by Graphing 3x+2y=4 2x-y=5

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