How do you solve the following system: x-y=3 , 4x-5y-23=0 ?

1 Answer
Mar 15, 2016

-4*(x - y) = -4*3
+4x - 5y = 23


-y = 11 or y = -11

-5(x - y) = -5*3
+4x - 5y = 23


-x = 8 or x = -8

Therefore, x = -8 and y = - 11

Explanation:

To solve this problem, you must first solve for one variable (x) and then the other (y). To solve for y, we eliminate the x variable by multiplying the first equation by -4 on both sides:

-4(x - y) = -4*3 ----> -4x +4y = -12

Then we add the two equations:

-4x + 4y = -12
+4x - 5y = 23

This gives us (-4x + 4x) + (4y - 5y) = (23-12) = -y = 11 or y = -11

To solve for x we then eliminate the y variable by multiplying the first equation by -5 on both sides:

-5(x - y) = -5*3 ----> -5x + 5y = -15

Then we add the two equations:

-5x + 5y = -15
+ 4x - 5y = 23

This gives us (-5x + 4x) + (5y - 5y) = 8 = -x = 8 or x = -8

You can check the answer by substituting -8 for x and -11 for y, and you will find that both equations are satisfied.