Final answer:
The question requires solving a system of equations using addition/elimination. After manipulating the second equation and combining them, x is found to be -6. Substituting x into one of the original equations then gives y as -2.
Step-by-step explanation:
The question involves solving a system of linear equations using the addition/elimination method. To solve the given equations 2x - 7y = 2 and 3x + y = -20, we need to manipulate the equations in such a way that adding them will eliminate one of the variables.
First, we can multiply the second equation by 7 to make the coefficients of y equal and opposite in sign:
7(3x + y) = 7(-20)
21x + 7y = -140
Now add the new equation to the first one:
(2x - 7y) + (21x + 7y) = 2 - 140
23x = -138
We can now solve for x:
x = -138 / 23
x = -6
Substitute x back into one of the original equations to solve for y, for example, the second equation:
3(-6) + y = -20
y = -2
Hence X = -6 and Y = -2.