Solve using elimination. -x – 3y = -11 -7x – 6y = -17 Find the values of x and y.

To solve the system of equations using elimination, follow these steps:

1. Write down the equations:

[

-x – 3y = -11 quad (1)

]

[

-7x – 6y = -17 quad (2)

]

2. Eliminate one variable: To eliminate ( x ), we can multiply equation (1) by 7:

[

7(-x – 3y) = 7(-11) quad Rightarrow quad -7x – 21y = -77 quad (3)

]

Now we have:

[

-7x – 21y = -77 quad (3)

]

[

-7x – 6y = -17 quad (2)

]

3. Subtract equation (2) from equation (3):

[

(-7x – 21y) – (-7x – 6y) = -77 – (-17)

]

This simplifies to:

[

-21y + 6y = -77 + 17 quad Rightarrow quad -15y = -60

]

4. Solve for ( y ):

[

y = frac{-60}{-15} = 4

]

5