Solve the System of Equations y=5x+13 y=x+45

$y = 5 x + 13$ $y = x + 45$

Step 1

Eliminate the equal sides of each equation and combine.

$5 x + 13 = x + 45$

Step 2

Solve $5 x + 13 = x + 45$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$5 x + 13 - x = 45$

Subtract $x$ from $5 x$ .

$4 x + 13 = 45$

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

Subtract $13$ from both sides of the equation.

$4 x = 45 - 13$

Subtract $13$ from $45$ .

$4 x = 32$

Divide each term in $4 x = 32$ by $4$ and simplify.

Divide each term in $4 x = 32$ by $4$ .

$\frac{4 x}{4} = \frac{32}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{32}{4}$

Divide $x$ by $1$ .

$x = \frac{32}{4}$

Simplify the right side.

Divide $32$ by $4$ .

$x = 8$

Step 3

Evaluate $y$ when $x = 8$ .

Substitute $8$ for $x$ .

$y = (8) + 45$

Substitute $8$ for $x$ in $y = (8) + 45$ and solve for $y$ .

Remove parentheses.

$y = 8 + 45$

Remove parentheses.

$y = (8) + 45$

Add $8$ and $45$ .

$y = 53$

Step 4

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

$(8, 53)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(8, 53)$

Equation Form:

$x = 8, y = 53$

Step 6

Solve the System of Equations y=5x+13 y=x+45

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