Question

Solving Systems by elimination. Solve the system-6x + 6y = 6-6x +3y = -12

Answer 1

We have the next system of equations:

`\begin{gathered} -6x+6y=6\text{ (eq. 1)} \\ -6x+3y=-12\text{ (eq. 2)} \end{gathered}`

Subtracting equation 2 to equation 1, we get:

Isolating y from equation 3:

`\begin{gathered} (3y)/(3)=(18)/(3) \\ y=6 \end{gathered}`

Substituting y = 6 into equation 1 and solving for x:

`\begin{gathered} -6x+6\cdot6=6 \\ -6x+36=6 \\ -6x+36-36=6-36 \\ -6x=-30 \\ (-6x)/(-6)=(-30)/(-6) \\ x=5 \end{gathered}`

The solution is the point (5, 6)