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

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

Step 1

Subtract $y$ from both sides of the equation.

$x = - 3 - y$

$2 x - y = 6$

Step 2

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

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

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

$x = - 3 - y$

Simplify the left side.

Simplify $2 (- 3 - y) - y$ .

Simplify each term.

Apply the distributive property.

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

$x = - 3 - y$

Multiply $2$ by $- 3$ .

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

$x = - 3 - y$

Multiply $- 1$ by $2$ .

$- 6 - 2 y - y = 6$

$x = - 3 - y$

$- 6 - 2 y - y = 6$

$x = - 3 - y$

Subtract $y$ from $- 2 y$ .

$- 6 - 3 y = 6$

$x = - 3 - y$

$- 6 - 3 y = 6$

$x = - 3 - y$

$- 6 - 3 y = 6$

$x = - 3 - y$

$- 6 - 3 y = 6$

$x = - 3 - y$

Step 3

Solve for $y$ in $- 6 - 3 y = 6$ .

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

Add $6$ to both sides of the equation.

$- 3 y = 6 + 6$

$x = - 3 - y$

Add $6$ and $6$ .

$- 3 y = 12$

$x = - 3 - y$

$- 3 y = 12$

$x = - 3 - y$

Divide each term in $- 3 y = 12$ by $- 3$ and simplify.

Divide each term in $- 3 y = 12$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

$x = - 3 - y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

$x = - 3 - y$

Divide $y$ by $1$ .

$y = \frac{12}{- 3}$

$x = - 3 - y$

$y = \frac{12}{- 3}$

$x = - 3 - y$

$y = \frac{12}{- 3}$

$x = - 3 - y$

Simplify the right side.

Divide $12$ by $- 3$ .

$y = - 4$

$x = - 3 - y$

$y = - 4$

$x = - 3 - y$

$y = - 4$

$x = - 3 - y$

$y = - 4$

$x = - 3 - y$

Step 4

Replace all occurrences of $y$ with $- 4$ in each equation.

Replace all occurrences of $y$ in $x = - 3 - y$ with $- 4$ .

$x = - 3 - (- 4)$

$y = - 4$

Simplify the right side.

Simplify $- 3 - (- 4)$ .

Multiply $- 1$ by $- 4$ .

$x = - 3 + 4$

$y = - 4$

Add $- 3$ and $4$ .

$x = 1$

$y = - 4$

$x = 1$

$y = - 4$

$x = 1$

$y = - 4$

$x = 1$

$y = - 4$

Step 5

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

$(1, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, - 4)$

Equation Form:

$x = 1, y = - 4$

Step 7

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

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