Solve the System of Equations x+2y=13 -x+y=5

$x + 2 y = 13$ $- x + y = 5$

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

$x = 13 - 2 y$

$- x + y = 5$

Replace all occurrences of $x$ with $13 - 2 y$ in each equation.

Replace all occurrences of $x$ in $- x + y = 5$ with $13 - 2 y$ .

$- (13 - 2 y) + y = 5$

$x = 13 - 2 y$

Simplify the left side.

Simplify $- (13 - 2 y) + y$ .

Simplify each term.

Apply the distributive property.

$- 1 \cdot 13 - (- 2 y) + y = 5$

$x = 13 - 2 y$

Multiply $- 1$ by $13$ .

$- 13 - (- 2 y) + y = 5$

$x = 13 - 2 y$

Multiply $- 2$ by $- 1$ .

$- 13 + 2 y + y = 5$

$x = 13 - 2 y$

$- 13 + 2 y + y = 5$

$x = 13 - 2 y$

Add $2 y$ and $y$ .

$- 13 + 3 y = 5$

$x = 13 - 2 y$

$- 13 + 3 y = 5$

$x = 13 - 2 y$

$- 13 + 3 y = 5$

$x = 13 - 2 y$

$- 13 + 3 y = 5$

$x = 13 - 2 y$

Solve for $y$ in $- 13 + 3 y = 5$ .

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

Add $13$ to both sides of the equation.

$3 y = 5 + 13$

$x = 13 - 2 y$

Add $5$ and $13$ .

$3 y = 18$

$x = 13 - 2 y$

$3 y = 18$

$x = 13 - 2 y$

Divide each term in $3 y = 18$ by $3$ and simplify.

Divide each term in $3 y = 18$ by $3$ .

$\frac{3 y}{3} = \frac{18}{3}$

$x = 13 - 2 y$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{18}{3}$

$x = 13 - 2 y$

Divide $y$ by $1$ .

$y = \frac{18}{3}$

$x = 13 - 2 y$

$y = \frac{18}{3}$

$x = 13 - 2 y$

$y = \frac{18}{3}$

$x = 13 - 2 y$

Simplify the right side.

Divide $18$ by $3$ .

$y = 6$

$x = 13 - 2 y$

$y = 6$

$x = 13 - 2 y$

$y = 6$

$x = 13 - 2 y$

$y = 6$

$x = 13 - 2 y$

Replace all occurrences of $y$ with $6$ in each equation.

Replace all occurrences of $y$ in $x = 13 - 2 y$ with $6$ .

$x = 13 - 2 \cdot 6$

$y = 6$

Simplify the right side.

Simplify $13 - 2 \cdot 6$ .

Multiply $- 2$ by $6$ .

$x = 13 - 12$

$y = 6$

Subtract $12$ from $13$ .

$x = 1$

$y = 6$

$x = 1$

$y = 6$

$x = 1$

$y = 6$

$x = 1$

$y = 6$

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

$(1, 6)$

The result can be shown in multiple forms.

Point Form:

$(1, 6)$

Equation Form:

$x = 1, y = 6$

Solve the System of Equations x+2y=13 -x+y=5

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