Solve the System of Equations x=2y-8 4x+y=13

$x = 2 y - 8$ $4 x + y = 13$

Replace all occurrences of $x$ with $2 y - 8$ in each equation.

Replace all occurrences of $x$ in $4 x + y = 13$ with $2 y - 8$ .

$4 (2 y - 8) + y = 13$

$x = 2 y - 8$

Simplify the left side.

Simplify $4 (2 y - 8) + y$ .

Simplify each term.

Apply the distributive property.

$4 (2 y) + 4 \cdot - 8 + y = 13$

$x = 2 y - 8$

Multiply $2$ by $4$ .

$8 y + 4 \cdot - 8 + y = 13$

$x = 2 y - 8$

Multiply $4$ by $- 8$ .

$8 y - 32 + y = 13$

$x = 2 y - 8$

$8 y - 32 + y = 13$

$x = 2 y - 8$

Add $8 y$ and $y$ .

$9 y - 32 = 13$

$x = 2 y - 8$

$9 y - 32 = 13$

$x = 2 y - 8$

$9 y - 32 = 13$

$x = 2 y - 8$

$9 y - 32 = 13$

$x = 2 y - 8$

Solve for $y$ in $9 y - 32 = 13$ .

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

Add $32$ to both sides of the equation.

$9 y = 13 + 32$

$x = 2 y - 8$

Add $13$ and $32$ .

$9 y = 45$

$x = 2 y - 8$

$9 y = 45$

$x = 2 y - 8$

Divide each term in $9 y = 45$ by $9$ and simplify.

Divide each term in $9 y = 45$ by $9$ .

$\frac{9 y}{9} = \frac{45}{9}$

$x = 2 y - 8$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{45}{9}$

$x = 2 y - 8$

Divide $y$ by $1$ .

$y = \frac{45}{9}$

$x = 2 y - 8$

$y = \frac{45}{9}$

$x = 2 y - 8$

$y = \frac{45}{9}$

$x = 2 y - 8$

Simplify the right side.

Divide $45$ by $9$ .

$y = 5$

$x = 2 y - 8$

$y = 5$

$x = 2 y - 8$

$y = 5$

$x = 2 y - 8$

$y = 5$

$x = 2 y - 8$

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

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

$x = 2 (5) - 8$

$y = 5$

Simplify the right side.

Simplify $2 (5) - 8$ .

Multiply $2$ by $5$ .

$x = 10 - 8$

$y = 5$

Subtract $8$ from $10$ .

$x = 2$

$y = 5$

$x = 2$

$y = 5$

$x = 2$

$y = 5$

$x = 2$

$y = 5$

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

$(2, 5)$

The result can be shown in multiple forms.

Point Form:

$(2, 5)$

Equation Form:

$x = 2, y = 5$

Solve the System of Equations x=2y-8 4x+y=13

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