use linear combinations to solve these system.

3x+2y=22
9x-8y=-4

-9x-6y=-66 Multiplied top equ. by -3

9x-8y=-4 Cancel x's
-14y=-70
y=5
Then plug in the y to find the x in an equation. Be sure to check by plugging both in after.

To solve this system of equations using linear combinations (also known as the method of elimination), follow these steps:

Step 1: Multiply one or both equations by suitable constants so that the coefficients in front of one variable are the same (or multiples of each other).

In this case, we can see that by multiplying the first equation by 3 and the second equation by 1, we can achieve matching coefficients for the x term.

Multiplying the first equation by 3:
3(3x + 2y) = 3(22)
9x + 6y = 66

Multiplying the second equation by 1:
1(9x - 8y) = 1(-4)
9x - 8y = -4

Step 2: Add or subtract the equations to eliminate one variable. In this case, we want to eliminate the x variable.

Subtracting the second equation from the first equation:
(9x + 6y) - (9x - 8y) = (66) - (-4)
9x + 6y - 9x + 8y = 66 + 4
14y = 70

Step 3: Solve the resulting equation for the remaining variable.

Dividing both sides of the equation by 14:
14y/14 = 70/14
y = 5

Step 4: Substitute the value of y back into one of the original equations to solve for x.

Using the first equation:
3x + 2y = 22
3x + 2(5) = 22
3x + 10 = 22
3x = 22 - 10
3x = 12
x = 4

Step 5: Check the solution of the system by substituting the values of x and y back into both original equations.

First equation:
3x + 2y = 22
3(4) + 2(5) = 22
12 + 10 = 22
22 = 22 (true)

Second equation:
9x - 8y = -4
9(4) - 8(5) = -4
36 - 40 = -4
-4 = -4 (true)

Therefore, the solution to the system of equations is x = 4, y = 5.