Solve by Substitution y=2x y=5x-30

$y = 2 x$ $y = 5 x - 30$

Step 1

Eliminate the equal sides of each equation and combine.

$2 x = 5 x - 30$

Step 2

Solve $2 x = 5 x - 30$ for $x$ .

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

Subtract $5 x$ from both sides of the equation.

$2 x - 5 x = - 30$

Subtract $5 x$ from $2 x$ .

$- 3 x = - 30$

Divide each term in $- 3 x = - 30$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 30$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 30}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 30}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 30}{- 3}$

Simplify the right side.

Divide $- 30$ by $- 3$ .

$x = 10$

Step 3

Evaluate $y$ when $x = 10$ .

Substitute $10$ for $x$ .

$y = 5 (10) - 30$

Simplify $5 (10) - 30$ .

Multiply $5$ by $10$ .

$y = 50 - 30$

Subtract $30$ from $50$ .

$y = 20$

Step 4

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

$(10, 20)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(10, 20)$

Equation Form:

$x = 10, y = 20$

Step 6