To use the linear combination method to solve the system of equations:
2x – 3y = 13
3x + y = -8
We can multiply the second equation by 3 to get:
9x + 3y = -24
Now we can add this equation to the first equation to eliminate the y term:
2x – 3y + 9x + 3y = 13 - 24
Simplifying the left-hand side and the right-hand side of the equation:
11x = -11
Finally, we can solve for x:
x = -1
Substitute x = -1 in either of the original equations:
2x – 3y = 13
2(-1) - 3y = 13
-2 - 3y = 13
-3y = 15
y = -5
Therefore, the solution to the system of equations is x = -1 and y = -5.
Explanation: We used the linear combination method to eliminate one of the variables by adding the two equations together. Then, we solved for the remaining variable and substituted the value back into one of the original equations to solve for the other variable.