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

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

Step 1

Divide each term in $2 y = 5 x + 4$ by $2$ and simplify.

Divide each term in $2 y = 5 x + 4$ by $2$ .

$\frac{2 y}{2} = \frac{5 x}{2} + \frac{4}{2}$

$y = 3 x + 2$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{5 x}{2} + \frac{4}{2}$

$y = 3 x + 2$

Divide $y$ by $1$ .

$y = \frac{5 x}{2} + \frac{4}{2}$

$y = 3 x + 2$

$y = \frac{5 x}{2} + \frac{4}{2}$

$y = 3 x + 2$

$y = \frac{5 x}{2} + \frac{4}{2}$

$y = 3 x + 2$

Simplify the right side.

Divide $4$ by $2$ .

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

$y = 3 x + 2$

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

$y = 3 x + 2$

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

$y = 3 x + 2$

Step 2

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

$(0, 2)$

Step 3