-3x+y=-2
-2=7x-y
To find the solution to this system of equations, we can use one of several methods - graphing, substitution, or elimination. Let's use the elimination method in this case.
First, let's multiply the second equation by -1 to make the coefficient of y the same as the first equation. This gives us:
-2 = 7x - y
Multiply every term in the equation by -1:
2 = -7x + y
Now we have two equations:
-3x + y = -2
-7x + y = 2
To eliminate the y-term, we can subtract the second equation from the first equation. This will cancel out the y-term:
(-3x + y) - (-7x + y) = (-2) - (2)
Simplify:
-3x + y + 7x - y = -2 - 2
Combine like terms:
-3x + 7x = -4
Simplify further:
4x = -4
Divide both sides by 4:
x = -4/4
Simplify:
x = -1
Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
-3(-1) + y = -2
Simplify:
3 + y = -2
Subtract 3 from both sides:
y = -2 - 3
Simplify:
y = -5
So the solution to the system of equations is x = -1 and y = -5.