What is the solution to the following system of equations?

Question

5x+2y=-4
-5x+4y=22

Answer 1

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

First, let's multiply the first equation by 2 to eliminate the x term:
10x + 4y = -8

Now, let's add this equation to the second equation:
(-5x + 4y) + (10x + 4y) = 22 + (-8)
5x + 8y = 14

Now we have the following system of equations:
5x + 8y = 14
-5x + 4y = 22

Next, let's multiply the second equation by 2 to eliminate the x term:
-10x + 8y = 44

Now, let's add this equation to the first equation:
(5x + 8y) + (-10x + 8y) = 14 + 44
-5x + 16y = 58

Now we have the following system of equations:
-5x + 16y = 58
-5x + 4y = 22

Since the x terms have the same coefficient, we can subtract the second equation from the first equation:
(-5x + 16y) - (-5x + 4y) = 58 - 22
5x - 5x + 16y - 4y = 36y = 36
36y = 36

Dividing both sides of the equation by 36, we find:
y = 1

Substituting this back into the second equation, we can solve for x:
-5x + 4(1) = 22
-5x + 4 = 22
-5x = 18
x = -18/5

Therefore, the solution to the system of equations is x = -18/5 and y = 1.