Question

solve the system of equations: 5x+2y=14 , x-6y=22

Answer 1

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

First, we will rewrite the equations in standard form:

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

Next, we will multiply equation (2) by 5 in order to get the coefficients of x to be the same in both equations:

5(x - 6y) = 5(22)
5x - 30y = 110

Now we will rewrite the new equation:
5x - 30y = 110 ... (3)
5x + 2y = 14 ... (1)

Now we will subtract equation (1) from equation (3) in order to eliminate x:

(5x - 30y) - (5x + 2y) = 110 - 14
-32y = 96

Now we can solve for y:
y = -3

Now that we have found the value of y, we can substitute it back into either equation (1) or (2) to solve for x.

Let's substitute y = -3 into equation (1):
5x + 2(-3) = 14
5x - 6 = 14
5x = 20
x = 4

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