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

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

Step 1

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

Step 2

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Step 3

Solve one of the equations for $y$ .

Subtract $3 x$ from both sides of the equation.

$- y = 6 - 3 x$

Divide each term in $- y = 6 - 3 x$ by $- 1$ and simplify.

Divide each term in $- y = 6 - 3 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 1$ .

$y = - 6 + \frac{- 3 x}{- 1}$

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

$y = - 6 - 1 \cdot (- 3 x)$

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

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

Multiply $- 3$ by $- 1$ .

$y = - 6 + 3 x$

Step 4

The solution is the set of ordered pairs that make $y = - 6 + 3 x$ true.

$(x, - 6 + 3 x)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(x, - 6 + 3 x)$

Equation Form:

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

Step 6