Question

Solve the system of equations

5x+2y=14
x-6y=22

Answer 1

To solve this system of equations, we can use the method of substitution or elimination.

Using the method of substitution:
We can solve the second equation for x in terms of y:
x = 22 + 6y.

Now we substitute this expression for x into the first equation:
5(22 + 6y) + 2y = 14.
Distribute the 5:
110 + 30y + 2y = 14.
Combine like terms:
32y + 110 = 14.
Subtract 110 from both sides:
32y = -96.
Divide both sides by 32:
y = -3.

Now substitute this value of y back into the second equation to solve for x:
x - 6(-3) = 22.
Multiply:
x + 18 = 22.
Subtract 18 from both sides:
x = 4.

The solution to the system of equations is x = 4 and y = -3.