Solve by Substitution y=2x+8 , y=3x-1

$y = 2 x + 8$ , $y = 3 x - 1$

Step 1

Eliminate the equal sides of each equation and combine.

$2 x + 8 = 3 x - 1$

Step 2

Solve $2 x + 8 = 3 x - 1$ for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$2 x + 8 - 3 x = - 1$

Subtract $3 x$ from $2 x$ .

$- x + 8 = - 1$

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

Subtract $8$ from both sides of the equation.

$- x = - 1 - 8$

Subtract $8$ from $- 1$ .

$- x = - 9$

Divide each term in $- x = - 9$ by $- 1$ and simplify.

Divide each term in $- x = - 9$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 9}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 9}{- 1}$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$x = 9$

Step 3

Evaluate $y$ when $x = 9$ .

Substitute $9$ for $x$ .

$y = 3 (9) - 1$

Simplify $3 (9) - 1$ .

Multiply $3$ by $9$ .

$y = 27 - 1$

Subtract $1$ from $27$ .

$y = 26$

Step 4

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

$(9, 26)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(9, 26)$

Equation Form:

$x = 9, y = 26$

Step 6

Solve by Substitution y=2x+8 , y=3x-1

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