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

2 Answers
Angus L.
Apr 13, 2018

(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)

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