Question

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

Answer 1

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

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`-y = 11 or y = -11`

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

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`-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.