The solution to the system of equations is (8, 10).
Identify the two equations that represent the two lines.
In this case, the two equations are:
y = 2x - 6
y = -1/2x - 6
Choose a method to solve the system of equations.
There are several methods to solve a system of equations. In this case, we will use elimination.
Eliminate one of the variables.
To eliminate y, we can add the two equations together.
y = 2x - 6
+ y = -1/2x - 6
Adding the two equations together, we get:
3/2x - 12 = 0
Solve for the remaining variable.
Dividing both sides by 3/2, we get:
x = 8
Substitute the value of the solved variable into one of the original equations to solve for the other variable.
Substituting x = 8 into the first equation, we get:
y = 2(8) - 6
y = 16 - 6
y = 10
Check your answer.
To check our answer, we can substitute x = 8 and y = 10 into both of the original equations. We should get the same value for y in both equations.
y = 2x - 6
y = 2(8) - 6
y = 16 - 6
y = 10
y = -1/2x - 6
y = -1/2(8) - 6
y = -4 - 6
y = 10
Therefore, the solution to the system of equations is (8, 10).