Final answer:
The solution to the system of equations is x = -3 and y = -7. This is found by first using the elimination method to find the value of x and then substituting the found value of x into one of the original equations to find the value of y.
Step-by-step explanation:
To solve the system of equations using elimination, we have the following two equations:
-2x - y = 13
7x + 3y = -42
We need to eliminate one variable. Let's eliminate y. To do this, we can multiply the first equation by 3 to make the coefficients of y equal but opposite in sign:
-2x * 3 -> -6x
-y * 3 -> -3y
13 * 3 -> 39
Now our equations are:
-6x - 3y = 39
7x + 3y = -42
Adding these two equations together:
-6x + 7x = x
-3y + 3y = 0
39 + (-42) = -3
So, x = -3.
Now, substitute x = -3 into the first original equation:
-2(-3) - y = 13
6 - y = 13
Subtract 6 from both sides:
-y = 13 - 6
-y = 7
Divide both sides by -1:
y = -7
The solution to the system of equations is x = -3 and y = -7.