Final answer:
To solve the linear equations 2x - y = -2 and x - 2y = -16 by elimination, multiply the first equation by 2 to match y's coefficient, add both equations to eliminate y, solve for x, and then substitute x back into one of the equations to find y. The solution is x = -4 and y = -6.
Step-by-step explanation:
Step-by-Step Elimination Process:
First, look at the coefficients of y in both equations.
We want to make them the same so we can eliminate y by adding the equations.
We can multiply the first equation by 2 to get 4x - 2y = -4.
The second equation is already set with a -2y, so we don't need to change it.
Now, add the new first equation (4x - 2y = -4) and the second equation (x - 2y = -16) together.
The y terms cancel out, leaving us with 5x = -20.
Divide both sides of the equation by 5 to solve for x.
We get x = -4.
Substitute x = -4 back into one of the original equations to find the value of y.
Using 2x - y = -2, we substitute and get 2(-4) - y = -2, which simplifies to -8 - y = -2.
Add 8 to both sides of the equation to solve for y, giving us y = -6.
The solution to the system is x = -4 and y = -6.