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.

Answer 1

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.