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

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

Step 1

Solve for $x$ in $- x - 2 y = 6$ .

Add $2 y$ to both sides of the equation.

$- x = 6 + 2 y$

$2 x - y = 3$

Divide each term in $- x = 6 + 2 y$ by $- 1$ and simplify.

Divide each term in $- x = 6 + 2 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{6}{- 1} + \frac{2 y}{- 1}$

$2 x - y = 3$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{6}{- 1} + \frac{2 y}{- 1}$

$2 x - y = 3$

Divide $x$ by $1$ .

$x = \frac{6}{- 1} + \frac{2 y}{- 1}$

$2 x - y = 3$

$x = \frac{6}{- 1} + \frac{2 y}{- 1}$

$2 x - y = 3$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 1$ .

$x = - 6 + \frac{2 y}{- 1}$

$2 x - y = 3$

Move the negative one from the denominator of $\frac{2 y}{- 1}$ .

$x = - 6 - 1 \cdot (2 y)$

$2 x - y = 3$

Rewrite $- 1 \cdot (2 y)$ as $- (2 y)$ .

$x = - 6 - (2 y)$

$2 x - y = 3$

Multiply $2$ by $- 1$ .

$x = - 6 - 2 y$

$2 x - y = 3$

$x = - 6 - 2 y$

$2 x - y = 3$

$x = - 6 - 2 y$

$2 x - y = 3$

$x = - 6 - 2 y$

$2 x - y = 3$

$x = - 6 - 2 y$

$2 x - y = 3$

Step 2

Replace all occurrences of $x$ with $- 6 - 2 y$ in each equation.

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

$2 (- 6 - 2 y) - y = 3$

$x = - 6 - 2 y$

Simplify the left side.

Simplify $2 (- 6 - 2 y) - y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 6 + 2 (- 2 y) - y = 3$

$x = - 6 - 2 y$

Multiply $2$ by $- 6$ .

$- 12 + 2 (- 2 y) - y = 3$

$x = - 6 - 2 y$

Multiply $- 2$ by $2$ .

$- 12 - 4 y - y = 3$

$x = - 6 - 2 y$

$- 12 - 4 y - y = 3$

$x = - 6 - 2 y$

Subtract $y$ from $- 4 y$ .

$- 12 - 5 y = 3$

$x = - 6 - 2 y$

$- 12 - 5 y = 3$

$x = - 6 - 2 y$

$- 12 - 5 y = 3$

$x = - 6 - 2 y$

$- 12 - 5 y = 3$

$x = - 6 - 2 y$

Step 3

Solve for $y$ in $- 12 - 5 y = 3$ .

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

Add $12$ to both sides of the equation.

$- 5 y = 3 + 12$

$x = - 6 - 2 y$

Add $3$ and $12$ .

$- 5 y = 15$

$x = - 6 - 2 y$

$- 5 y = 15$

$x = - 6 - 2 y$

Divide each term in $- 5 y = 15$ by $- 5$ and simplify.

Divide each term in $- 5 y = 15$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{15}{- 5}$

$x = - 6 - 2 y$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{15}{- 5}$

$x = - 6 - 2 y$

Divide $y$ by $1$ .

$y = \frac{15}{- 5}$

$x = - 6 - 2 y$

$y = \frac{15}{- 5}$

$x = - 6 - 2 y$

$y = \frac{15}{- 5}$

$x = - 6 - 2 y$

Simplify the right side.

Divide $15$ by $- 5$ .

$y = - 3$

$x = - 6 - 2 y$

$y = - 3$

$x = - 6 - 2 y$

$y = - 3$

$x = - 6 - 2 y$

$y = - 3$

$x = - 6 - 2 y$

Step 4

Replace all occurrences of $y$ with $- 3$ in each equation.

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

$x = - 6 - 2 \cdot - 3$

$y = - 3$

Simplify the right side.

Simplify $- 6 - 2 \cdot - 3$ .

Multiply $- 2$ by $- 3$ .

$x = - 6 + 6$

$y = - 3$

Add $- 6$ and $6$ .

$x = 0$

$y = - 3$

$x = 0$

$y = - 3$

$x = 0$

$y = - 3$

$x = 0$

$y = - 3$

Step 5

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

$(0, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, - 3)$

Equation Form:

$x = 0, y = - 3$

Step 7

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

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