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

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

Step 1

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

$2 y = 4 - 3 x$

$5 x - 4 y = 3$

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 $2$ .

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

$5 x - 4 y = 3$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$5 x - 4 y = 3$

Divide $y$ by $1$ .

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

$5 x - 4 y = 3$

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

$5 x - 4 y = 3$

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

$5 x - 4 y = 3$

Simplify the right side.

Simplify each term.

Divide $4$ by $2$ .

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

$5 x - 4 y = 3$

Move the negative in front of the fraction.

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

$5 x - 4 y = 3$

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

$5 x - 4 y = 3$

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

$5 x - 4 y = 3$

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

$5 x - 4 y = 3$

Step 3

Subtract $5 x$ from both sides of the equation.

$- 4 y = 3 - 5 x$

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

Step 4

Divide each term in $- 4 y = 3 - 5 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 3 - 5 x$ by $- 4$ .

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

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

Divide $y$ by $1$ .

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

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

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

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

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

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

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

Dividing two negative values results in a positive value.

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

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

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

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

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

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

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

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

Step 5

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

$(1, \frac{1}{2})$

Step 6

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

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