Solve the System of Equations 2x-5y=8 5y=-2x+8

$2 x - 5 y = 8$ $5 y = - 2 x + 8$

Step 1

Divide each term in $5 y = - 2 x + 8$ by $5$ and simplify.

Divide each term in $5 y = - 2 x + 8$ by $5$ .

$\frac{5 y}{5} = \frac{- 2 x}{5} + \frac{8}{5}$

$2 x - 5 y = 8$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 2 x}{5} + \frac{8}{5}$

$2 x - 5 y = 8$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{5} + \frac{8}{5}$

$2 x - 5 y = 8$

$y = \frac{- 2 x}{5} + \frac{8}{5}$

$2 x - 5 y = 8$

$y = \frac{- 2 x}{5} + \frac{8}{5}$

$2 x - 5 y = 8$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{2 x}{5} + \frac{8}{5}$

$2 x - 5 y = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$2 x - 5 y = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$2 x - 5 y = 8$

Step 2

Replace all occurrences of $y$ with $- \frac{2 x}{5} + \frac{8}{5}$ in each equation.

Replace all occurrences of $y$ in $2 x - 5 y = 8$ with $- \frac{2 x}{5} + \frac{8}{5}$ .

$2 x - 5 (- \frac{2 x}{5} + \frac{8}{5}) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Simplify the left side.

Simplify $2 x - 5 (- \frac{2 x}{5} + \frac{8}{5})$ .

Simplify each term.

Apply the distributive property.

$2 x - 5 (- \frac{2 x}{5}) - 5 (\frac{8}{5}) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2 x}{5}$ into the numerator.

$2 x - 5 \frac{- 2 x}{5} - 5 (\frac{8}{5}) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Factor $5$ out of $- 5$ .

$2 x + 5 (- 1) (\frac{- 2 x}{5}) - 5 (\frac{8}{5}) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Cancel the common factor.

$2 x + 5 \cdot (- 1 \frac{- 2 x}{5}) - 5 (\frac{8}{5}) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Rewrite the expression.

$2 x - 1 (- 2 x) - 5 (\frac{8}{5}) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$2 x - 1 (- 2 x) - 5 (\frac{8}{5}) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Multiply $- 2$ by $- 1$ .

$2 x + 2 x - 5 (\frac{8}{5}) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$2 x + 2 x + 5 (- 1) (\frac{8}{5}) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Cancel the common factor.

$2 x + 2 x + 5 \cdot (- 1 (\frac{8}{5})) = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Rewrite the expression.

$2 x + 2 x - 1 \cdot 8 = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$2 x + 2 x - 1 \cdot 8 = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Multiply $- 1$ by $8$ .

$2 x + 2 x - 8 = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$2 x + 2 x - 8 = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Add $2 x$ and $2 x$ .

$4 x - 8 = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$4 x - 8 = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$4 x - 8 = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$4 x - 8 = 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Step 3

Solve for $x$ in $4 x - 8 = 8$ .

Move all terms not containing $x$ to the right side of the equation.

Add $8$ to both sides of the equation.

$4 x = 8 + 8$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Add $8$ and $8$ .

$4 x = 16$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$4 x = 16$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Divide each term in $4 x = 16$ by $4$ and simplify.

Divide each term in $4 x = 16$ by $4$ .

$\frac{4 x}{4} = \frac{16}{4}$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{16}{4}$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Divide $x$ by $1$ .

$x = \frac{16}{4}$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$x = \frac{16}{4}$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$x = \frac{16}{4}$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Simplify the right side.

Divide $16$ by $4$ .

$x = 4$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$x = 4$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$x = 4$

$y = - \frac{2 x}{5} + \frac{8}{5}$

$x = 4$

$y = - \frac{2 x}{5} + \frac{8}{5}$

Step 4

Replace all occurrences of $x$ with $4$ in each equation.

Replace all occurrences of $x$ in $y = - \frac{2 x}{5} + \frac{8}{5}$ with $4$ .

$y = - \frac{2 (4)}{5} + \frac{8}{5}$

$x = 4$

Simplify the right side.

Simplify $- \frac{2 (4)}{5} + \frac{8}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 2 \cdot 4 + 8}{5}$

$x = 4$

Simplify the expression.

Multiply $- 2$ by $4$ .

$y = \frac{- 8 + 8}{5}$

$x = 4$

Add $- 8$ and $8$ .

$y = \frac{0}{5}$

$x = 4$

Divide $0$ by $5$ .

$y = 0$

$x = 4$

$y = 0$

$x = 4$

$y = 0$

$x = 4$

$y = 0$

$x = 4$

$y = 0$

$x = 4$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(4, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 0)$

Equation Form:

$x = 4, y = 0$

Step 7

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