Solve by Graphing 2x+4y=20; 3x+2y=26

${\begin{cases} 2 x + 4 y = 20 \\ 3 x + 2 y = 26 \end{cases}$

Step 1

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

$4 y = 20 - 2 x$

$3 x + 2 y = 26$

Step 2

Divide each term in $4 y = 20 - 2 x$ by $4$ and simplify.

Divide each term in $4 y = 20 - 2 x$ by $4$ .

$\frac{4 y}{4} = \frac{20}{4} + \frac{- 2 x}{4}$

$3 x + 2 y = 26$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{20}{4} + \frac{- 2 x}{4}$

$3 x + 2 y = 26$

Divide $y$ by $1$ .

$y = \frac{20}{4} + \frac{- 2 x}{4}$

$3 x + 2 y = 26$

$y = \frac{20}{4} + \frac{- 2 x}{4}$

$3 x + 2 y = 26$

$y = \frac{20}{4} + \frac{- 2 x}{4}$

$3 x + 2 y = 26$

Simplify the right side.

Simplify each term.

Divide $20$ by $4$ .

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

$3 x + 2 y = 26$

Cancel the common factor of $- 2$ and $4$ .

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

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

$3 x + 2 y = 26$

Cancel the common factors.

Factor $2$ out of $4$ .

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

$3 x + 2 y = 26$

Cancel the common factor.

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

$3 x + 2 y = 26$

Rewrite the expression.

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

$3 x + 2 y = 26$

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

$3 x + 2 y = 26$

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

$3 x + 2 y = 26$

Move the negative in front of the fraction.

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

$3 x + 2 y = 26$

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

$3 x + 2 y = 26$

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

$3 x + 2 y = 26$

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

$3 x + 2 y = 26$

Step 3

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

$2 y = 26 - 3 x$

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

Step 4

Divide each term in $2 y = 26 - 3 x$ by $2$ and simplify.

Divide each term in $2 y = 26 - 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{26}{2} + \frac{- 3 x}{2}$

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{26}{2} + \frac{- 3 x}{2}$

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

Divide $y$ by $1$ .

$y = \frac{26}{2} + \frac{- 3 x}{2}$

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

$y = \frac{26}{2} + \frac{- 3 x}{2}$

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

$y = \frac{26}{2} + \frac{- 3 x}{2}$

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

Simplify the right side.

Simplify each term.

Divide $26$ by $2$ .

$y = 13 + \frac{- 3 x}{2}$

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

Move the negative in front of the fraction.

$y = 13 - \frac{3 x}{2}$

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

$y = 13 - \frac{3 x}{2}$

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

$y = 13 - \frac{3 x}{2}$

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

$y = 13 - \frac{3 x}{2}$

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

Step 5

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

$(8, 1)$

Step 6

Solve by Graphing 2x+4y=20; 3x+2y=26

Related Questions

Support LCMGCF.com by disabling your adblocker.