Question

Solve the system of equations: -5x - 2y = -18 and 3x + y = 11

Answer 1

To solve the system of equations:

-5x - 2y = -18

3x + y = 11

We can use the method of substitution or elimination. Let's use the elimination method:

First, we can multiply equation (2) by 2 to make the coefficients of y in both equations cancel each other out:

-5x - 2y = -18

6x + 2y = 22

Now, add equation (1) and equation (2) to eliminate the variable y:

(-5x - 2y) + (6x + 2y) = (-18 + 22)

This simplifies to:

1x = 4

Now, solve for x:

x = 4

Now that we have the value of x, we can substitute it back into equation (2) to solve for y:

3x + y = 11

3(4) + y = 11

12 + y = 11

Subtract 12 from both sides to solve for y:

y = 11 - 12

y = -1

So, the solution to the system of equations is:

x = 4

y = -1

Answer 2

x = 4

y = -1

Explanation:

-5x - 2y = -18

3x + y = 11

Isolate y from 3x + y = 11:

y = 11 - 3x

Substitute y in -5x - 2y = -18:

-5x - 2(11 - 3x) = -18

Distribute:

-5x - 22 + 6x = -18

Combine like terms:

x - 22 = -18

Add 22 to both sides:

x = 4

Now that we know what x is, replace it in 3x + y = 11:

3(4) + y = 11

12 + y = 11

Subtract 12 from both sides:

y = -1

Check your work with -5x - 2y = -18:

-5(4) - 2(-1) = -18

-20 + 2 = -18

Now with 3x + y = 11:

3(4) + (-1) = 11

12 - 1 = 11

They both work, therefore this is the correct answer