Answer:
To solve the system of equations:
2x - 9y = 26 ...(1)
6x - 2y = -22 ...(2)
We can use the method of substitution or elimination. Let's use the substitution method in this case.
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve equation (1) for x:
2x = 9y + 26
x = (9y + 26)/2
Step 2: Substitute the expression for x from step 1 into equation (2):
6((9y + 26)/2) - 2y = -22
Simplify the equation:
3(9y + 26) - 2y = -22
27y + 78 - 2y = -22
25y + 78 = -22
25y = -22 - 78
25y = -100
y = -100/25
y = -4
Step 3: Substitute the value of y into equation (1) to find x:
2x - 9(-4) = 26
2x + 36 = 26
2x = 26 - 36
2x = -10
x = -10/2
x = -5
So, the solution to the system of equations is x = -5 and y = -4.
Keep in mind that this is just one possible method for solving the system of equations. There are other methods like graphing or using matrices, but substitution is often a straightforward approach.