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

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

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

$y = 5 - 2 x$

$2 y = 2 x - 8$

Replace all occurrences of $y$ with $5 - 2 x$ in each equation.

Replace all occurrences of $y$ in $2 y = 2 x - 8$ with $5 - 2 x$ .

$2 (5 - 2 x) = 2 x - 8$

$y = 5 - 2 x$

Simplify the left side.

Simplify $2 (5 - 2 x)$ .

Apply the distributive property.

$2 \cdot 5 + 2 (- 2 x) = 2 x - 8$

$y = 5 - 2 x$

Multiply.

Multiply $2$ by $5$ .

$10 + 2 (- 2 x) = 2 x - 8$

$y = 5 - 2 x$

Multiply $- 2$ by $2$ .

$10 - 4 x = 2 x - 8$

$y = 5 - 2 x$

$10 - 4 x = 2 x - 8$

$y = 5 - 2 x$

$10 - 4 x = 2 x - 8$

$y = 5 - 2 x$

$10 - 4 x = 2 x - 8$

$y = 5 - 2 x$

$10 - 4 x = 2 x - 8$

$y = 5 - 2 x$

Solve for $x$ in $10 - 4 x = 2 x - 8$ .

Move all terms containing $x$ to the left side of the equation.

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

$10 - 4 x - 2 x = - 8$

$y = 5 - 2 x$

Subtract $2 x$ from $- 4 x$ .

$10 - 6 x = - 8$

$y = 5 - 2 x$

$10 - 6 x = - 8$

$y = 5 - 2 x$

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

Subtract $10$ from both sides of the equation.

$- 6 x = - 8 - 10$

$y = 5 - 2 x$

Subtract $10$ from $- 8$ .

$- 6 x = - 18$

$y = 5 - 2 x$

$- 6 x = - 18$

$y = 5 - 2 x$

Divide each term in $- 6 x = - 18$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 18$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 18}{- 6}$

$y = 5 - 2 x$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 18}{- 6}$

$y = 5 - 2 x$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 6}$

$y = 5 - 2 x$

$x = \frac{- 18}{- 6}$

$y = 5 - 2 x$

$x = \frac{- 18}{- 6}$

$y = 5 - 2 x$

Simplify the right side.

Divide $- 18$ by $- 6$ .

$x = 3$

$y = 5 - 2 x$

$x = 3$

$y = 5 - 2 x$

$x = 3$

$y = 5 - 2 x$

$x = 3$

$y = 5 - 2 x$

Replace all occurrences of $x$ with $3$ in each equation.

Replace all occurrences of $x$ in $y = 5 - 2 x$ with $3$ .

$y = 5 - 2 \cdot 3$

$x = 3$

Simplify the right side.

Simplify $5 - 2 \cdot 3$ .

Multiply $- 2$ by $3$ .

$y = 5 - 6$

$x = 3$

Subtract $6$ from $5$ .

$y = - 1$

$x = 3$

$y = - 1$

$x = 3$

$y = - 1$

$x = 3$

$y = - 1$

$x = 3$

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

$(3, - 1)$

The result can be shown in multiple forms.

Point Form:

$(3, - 1)$

Equation Form:

$x = 3, y = - 1$

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

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