Question

Solve the systems of equations.
5x + 2y = 14
x - 6y = 22

(___, ___)

Answer 1

To solve this system of equations, we can use the method of substitution or linear combination. Let's use the substitution method.

From the first equation:
5x + 2y = 14
y = (14 - 5x) / 2

Substitute this value of y into the second equation:
x - 6((14 - 5x) / 2) = 22
x - 42 + 15x = 44
16x - 42 = 44
16x = 86
x = 86 / 16
x = 5.375

Now substitute the value of x back into the first equation to find y:
5(5.375) + 2y = 14
26.875 + 2y = 14
2y = 14 - 26.875
2y = -12.875
y = -12.875 / 2
y = -6.4375

Therefore, the solution to the system of equations is (5.375, -6.4375).

Answer 2

wrong answer

Answer 3

My apologies. Let me try again:

Using the substitution method to solve the system of equations:

5x + 2y = 14 (1)
x - 6y = 22 (2)

From equation (2), we can express x in terms of y:
x = 22 + 6y (3)

Now, substitute the expression for x from equation (3) into equation (1):

5(22 + 6y) + 2y = 14
110 + 30y + 2y = 14
32y = -96
y = -96 / 32
y = -3

Now, substitute the value of y back into equation (3) to find x:
x = 22 + 6(-3)
x = 22 - 18
x = 4

Therefore, the correct solution to the system of equations is (4, -3).