Solve by Substitution y=5x-10 , y=3x+8

$y = 5 x - 10$ , $y = 3 x + 8$

Step 1

Eliminate the equal sides of each equation and combine.

$5 x - 10 = 3 x + 8$

Step 2

Solve $5 x - 10 = 3 x + 8$ for $x$ .

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

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

$5 x - 10 - 3 x = 8$

Subtract $3 x$ from $5 x$ .

$2 x - 10 = 8$

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

Add $10$ to both sides of the equation.

$2 x = 8 + 10$

Add $8$ and $10$ .

$2 x = 18$

Divide each term in $2 x = 18$ by $2$ and simplify.

Divide each term in $2 x = 18$ by $2$ .

$\frac{2 x}{2} = \frac{18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{18}{2}$

Divide $x$ by $1$ .

$x = \frac{18}{2}$

Simplify the right side.

Divide $18$ by $2$ .

$x = 9$

Step 3

Evaluate $y$ when $x = 9$ .

Substitute $9$ for $x$ .

$y = 3 (9) + 8$

Simplify $3 (9) + 8$ .

Multiply $3$ by $9$ .

$y = 27 + 8$

Add $27$ and $8$ .

$y = 35$

Step 4

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

$(9, 35)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(9, 35)$

Equation Form:

$x = 9, y = 35$

Step 6

Solve by Substitution y=5x-10 , y=3x+8

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