Question

Solve the system of equations.%0D%0A5x+2y=14%0D%0Ax−6y=22

Answer 1

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

Let's use the elimination method:

First, multiply the second equation by 5 to make the coefficients of x in both equations equal:

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

Now we have the system of equations:

5x + 2y = 14
5x - 30y = 110

Next, we'll add the two equations together to eliminate x:

(5x + 2y) + (5x - 30y) = 14 + 110
10x - 28y = 124

Now we can solve this new equation for x:

10x - 28y = 124
10x = 28y + 124
x = 28/10 y + 124/10
x = 2.8y + 12.4

Now that we have a value for x in terms of y, we can substitute this back into one of the original equations to solve for y:

5(2.8y + 12.4) + 2y = 14
14y + 62 + 2y = 14
16y + 62 = 14
16y = -48
y = -3

Now that we have a value for y, we can substitute y = -3 back into x = 2.8y + 12.4 to solve for x:

x = 2.8(-3) + 12.4
x = -8.4 + 12.4
x = 4

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