Solve by Substitution x=3y+7 , x=2y-1

$x = 3 y + 7$ , $x = 2 y - 1$

Step 1

Eliminate the equal sides of each equation and combine.

$3 y + 7 = 2 y - 1$

Step 2

Solve $3 y + 7 = 2 y - 1$ for $y$ .

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

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

$3 y + 7 - 2 y = - 1$

Subtract $2 y$ from $3 y$ .

$y + 7 = - 1$

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

Subtract $7$ from both sides of the equation.

$y = - 1 - 7$

Subtract $7$ from $- 1$ .

$y = - 8$

Step 3

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

Substitute $- 8$ for $y$ .

$x = 2 (- 8) - 1$

Simplify $2 (- 8) - 1$ .

Multiply $2$ by $- 8$ .

$x = - 16 - 1$

Subtract $1$ from $- 16$ .

$x = - 17$

Step 4

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

$(- 17, - 8)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 17, - 8)$

Equation Form:

$x = - 17, y = - 8$

Step 6