Question

How do you solve `2X-3Y=21` and `5X+4Y=-5`?

Answer 1

Answer 2

(3,-5)

Explanation:

I'm going to assume you are looking for the intersection of the two.
Lets start by solving both for y.
`2X-3Y=21`, therefore `3Y = 2X-21`, and `Y = (2X-21)/3`
`5X+4Y=-5`, `4Y=-5X-5` and `Y = -5/4(X+5)`
Now lets try seeing for what value of x, these two equations are equal (and therefore Y=Y)
`Y=Y, (2X-21)/3 = -5/4(X+1)`
`4(2X-21)=-15(X+1)`
`4(2X-21)+15(X+1)=0`
`8X-84+15X+15=0`
`23X-69=0`
And finally,
`X=3`
Now, lets find the value of y but inserting this x into either of the original equations!
`2X-3Y=21`
`2(3)-3Y=21`
`6-3Y=21`
`3Y=-15`
`Y=-5`
Therefore, the answer is (X,Y)=(3,-5)