Question

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

Answer 1

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

First, we can solve one equation for one variable and substitute it into the other equation.

From the second equation x - 6y = 22, we can solve for x:
x = 22 + 6y

Now, we substitute this expression for x into the first equation:
5(22 + 6y) + 2y = 14

Simplifying the equation:
110 + 30y + 2y = 14
32y = 14 - 110
32y = -96

Dividing both sides by 32:
y = -96/32
y = -3

Now, substitute this value of y into the expression for x:
x = 22 + 6(-3)
x = 22 - 18
x = 4

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