Solve by Substitution x-3y=6 , y=2x-22

$x - 3 y = 6$ , $y = 2 x - 22$

Step 1

Replace all occurrences of $y$ with $2 x - 22$ in each equation.

Replace all occurrences of $y$ in $x - 3 y = 6$ with $2 x - 22$ .

$x - 3 (2 x - 22) = 6$

$y = 2 x - 22$

Simplify the left side.

Simplify $x - 3 (2 x - 22)$ .

Simplify each term.

Apply the distributive property.

$x - 3 (2 x) - 3 \cdot - 22 = 6$

$y = 2 x - 22$

Multiply $2$ by $- 3$ .

$x - 6 x - 3 \cdot - 22 = 6$

$y = 2 x - 22$

Multiply $- 3$ by $- 22$ .

$x - 6 x + 66 = 6$

$y = 2 x - 22$

$x - 6 x + 66 = 6$

$y = 2 x - 22$

Subtract $6 x$ from $x$ .

$- 5 x + 66 = 6$

$y = 2 x - 22$

$- 5 x + 66 = 6$

$y = 2 x - 22$

$- 5 x + 66 = 6$

$y = 2 x - 22$

$- 5 x + 66 = 6$

$y = 2 x - 22$

Step 2

Solve for $x$ in $- 5 x + 66 = 6$ .

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

Subtract $66$ from both sides of the equation.

$- 5 x = 6 - 66$

$y = 2 x - 22$

Subtract $66$ from $6$ .

$- 5 x = - 60$

$y = 2 x - 22$

$- 5 x = - 60$

$y = 2 x - 22$

Divide each term in $- 5 x = - 60$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 60$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 60}{- 5}$

$y = 2 x - 22$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 60}{- 5}$

$y = 2 x - 22$

Divide $x$ by $1$ .

$x = \frac{- 60}{- 5}$

$y = 2 x - 22$

$x = \frac{- 60}{- 5}$

$y = 2 x - 22$

$x = \frac{- 60}{- 5}$

$y = 2 x - 22$

Simplify the right side.

Divide $- 60$ by $- 5$ .

$x = 12$

$y = 2 x - 22$

$x = 12$

$y = 2 x - 22$

$x = 12$

$y = 2 x - 22$

$x = 12$

$y = 2 x - 22$

Step 3

Replace all occurrences of $x$ with $12$ in each equation.

Replace all occurrences of $x$ in $y = 2 x - 22$ with $12$ .

$y = 2 (12) - 22$

$x = 12$

Simplify the right side.

Simplify $2 (12) - 22$ .

Multiply $2$ by $12$ .

$y = 24 - 22$

$x = 12$

Subtract $22$ from $24$ .

$y = 2$

$x = 12$

$y = 2$

$x = 12$

$y = 2$

$x = 12$

$y = 2$

$x = 12$

Step 4

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

$(12, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(12, 2)$

Equation Form:

$x = 12, y = 2$

Step 6

Solve by Substitution x-3y=6 , y=2x-22

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