Solve by Substitution y=10x-9 y=x+18

$y = 10 x - 9$ $y = x + 18$

Step 1

Eliminate the equal sides of each equation and combine.

$10 x - 9 = x + 18$

Step 2

Solve $10 x - 9 = x + 18$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$10 x - 9 - x = 18$

Subtract $x$ from $10 x$ .

$9 x - 9 = 18$

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

Add $9$ to both sides of the equation.

$9 x = 18 + 9$

Add $18$ and $9$ .

$9 x = 27$

Divide each term in $9 x = 27$ by $9$ and simplify.

Divide each term in $9 x = 27$ by $9$ .

$\frac{9 x}{9} = \frac{27}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{27}{9}$

Divide $x$ by $1$ .

$x = \frac{27}{9}$

Simplify the right side.

Divide $27$ by $9$ .

$x = 3$

Step 3

Evaluate $y$ when $x = 3$ .

Substitute $3$ for $x$ .

$y = (3) + 18$

Substitute $3$ for $x$ in $y = (3) + 18$ and solve for $y$ .

Remove parentheses.

$y = 3 + 18$

Remove parentheses.

$y = (3) + 18$

Add $3$ and $18$ .

$y = 21$

Step 4

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

$(3, 21)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(3, 21)$

Equation Form:

$x = 3, y = 21$

Step 6

Solve by Substitution y=10x-9 y=x+18

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