Solve by Linear Combination 2x+y=1 3x-y=-6

$2 x + y = 1$ $3 x - y = - 6$

Step 1

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

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$

Step 3

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

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

$2 (- 1) + y = 1$

Multiply $2$ by $- 1$ .

$- 2 + y = 1$

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

Add $2$ to both sides of the equation.

$y = 1 + 2$

Add $1$ and $2$ .

$y = 3$

Step 4

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

$(- 1, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, 3)$

Equation Form:

$x = - 1, y = 3$

Step 6