Solve by Graphing 4x+3y=29 2x-3y=1

$4 x + 3 y = 29$ $2 x - 3 y = 1$

Step 1

Subtract $4 x$ from both sides of the equation.

$3 y = 29 - 4 x$

$2 x - 3 y = 1$

Step 2

Divide each term in $3 y = 29 - 4 x$ by $3$ and simplify.

Divide each term in $3 y = 29 - 4 x$ by $3$ .

$\frac{3 y}{3} = \frac{29}{3} + \frac{- 4 x}{3}$

$2 x - 3 y = 1$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{29}{3} + \frac{- 4 x}{3}$

$2 x - 3 y = 1$

Divide $y$ by $1$ .

$y = \frac{29}{3} + \frac{- 4 x}{3}$

$2 x - 3 y = 1$

$y = \frac{29}{3} + \frac{- 4 x}{3}$

$2 x - 3 y = 1$

$y = \frac{29}{3} + \frac{- 4 x}{3}$

$2 x - 3 y = 1$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{29}{3} - \frac{4 x}{3}$

$2 x - 3 y = 1$

$y = \frac{29}{3} - \frac{4 x}{3}$

$2 x - 3 y = 1$

$y = \frac{29}{3} - \frac{4 x}{3}$

$2 x - 3 y = 1$

Step 3

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

$- 3 y = 1 - 2 x$

$y = \frac{29}{3} - \frac{4 x}{3}$

Step 4

Divide each term in $- 3 y = 1 - 2 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 1 - 2 x$ by $- 3$ .

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

$y = \frac{29}{3} - \frac{4 x}{3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$y = \frac{29}{3} - \frac{4 x}{3}$

Divide $y$ by $1$ .

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

$y = \frac{29}{3} - \frac{4 x}{3}$

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

$y = \frac{29}{3} - \frac{4 x}{3}$

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

$y = \frac{29}{3} - \frac{4 x}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

$y = \frac{29}{3} - \frac{4 x}{3}$

Dividing two negative values results in a positive value.

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

$y = \frac{29}{3} - \frac{4 x}{3}$

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

$y = \frac{29}{3} - \frac{4 x}{3}$

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

$y = \frac{29}{3} - \frac{4 x}{3}$

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

$y = \frac{29}{3} - \frac{4 x}{3}$

Step 5

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

$(5, 3)$

Step 6

Related Questions