Solve by Addition/Elimination x-y=6 -3y=x+22

$x - y = 6$ $- 3 y = x + 22$

Step 1

Subtract $x$ from both sides of the equation.

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

Step 2

Reorder the polynomial.

$- x - 3 y = 22$

$x - y = 6$

Step 3

Add the two equations together to eliminate $x$ from the system.

Step 4

Divide each term in $- 4 y = 28$ by $- 4$ and simplify.

Divide each term in $- 4 y = 28$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{28}{- 4}$

Divide $y$ by $1$ .

$y = \frac{28}{- 4}$

Simplify the right side.

Divide $28$ by $- 4$ .

$y = - 7$

Step 5

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$x - (- 7) = 6$

Multiply $- 1$ by $- 7$ .

$x + 7 = 6$

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

Subtract $7$ from both sides of the equation.

$x = 6 - 7$

Subtract $7$ from $6$ .

$x = - 1$

Step 6

The solution to the independent system of equations can be represented as a point.

$(- 1, - 7)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 1, - 7)$

Equation Form:

$x = - 1, y = - 7$

Step 8