Solve by Substitution y=3x+7 , y=x-9

$y = 3 x + 7$ , $y = x - 9$

Step 1

Eliminate the equal sides of each equation and combine.

$3 x + 7 = x - 9$

Step 2

Solve $3 x + 7 = x - 9$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$3 x + 7 - x = - 9$

Subtract $x$ from $3 x$ .

$2 x + 7 = - 9$

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

Subtract $7$ from both sides of the equation.

$2 x = - 9 - 7$

Subtract $7$ from $- 9$ .

$2 x = - 16$

Divide each term in $2 x = - 16$ by $2$ and simplify.

Divide each term in $2 x = - 16$ by $2$ .

$\frac{2 x}{2} = \frac{- 16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 16}{2}$

Divide $x$ by $1$ .

$x = \frac{- 16}{2}$

Simplify the right side.

Divide $- 16$ by $2$ .

$x = - 8$

Step 3

Evaluate $y$ when $x = - 8$ .

Substitute $- 8$ for $x$ .

$y = (- 8) - 9$

Substitute $- 8$ for $x$ in $y = (- 8) - 9$ and solve for $y$ .

Remove parentheses.

$y = - 8 - 9$

Remove parentheses.

$y = (- 8) - 9$

Subtract $9$ from $- 8$ .

$y = - 17$

Step 4

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

$(- 8, - 17)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 8, - 17)$

Equation Form:

$x = - 8, y = - 17$

Step 6

Solve by Substitution y=3x+7 , y=x-9

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