Solve the system of equations using elimination: minus, x, minus, y, equals, minus, 6−x−y=−6 and minus, 7, x, minus, y, equals, minus, 30−7x−y=−30.
To solve using elimination, we'll add the two equations together to eliminate the y terms.
Adding the equations gives:
(6 - x - y) + (-7x - y) = (-6) + (-30)
Combining like terms:
-8x - 2y = -36
Now we can solve for y by isolating it in one of the equations.
From the first equation, we have:
6 - x - y = -6
Rearranging the equation:
y = -6 - 6 + x
y = -12 + x
Substituting this expression for y in the second equation:
-8x - 2(-12 + x) = -36
Simplifying:
-8x + 24 - 2x = -36
Combine like terms:
-10x + 24 = -36
Subtract 24 from both sides:
-10x = -60
Divide both sides by -10:
x = 6
Now we can substitute this value of x back into one of the original equations to solve for y.
Using the first equation:
6 - (6) - y = -6
Simplifying:
-6 - y = -6
Add 6 to both sides:
-6 + 6 - y = 0
-y = 0
Divide both sides by -1:
y = 0
Therefore, the solution to the system of equations is x = 6 and y = 0.