How do you solve the system of equations 2x + 3y = 13 and 3x - 5y = - 9?

1 Answer
Apr 4, 2018

#(x,y)=(2,3)

Explanation:

2x=13-3y
x=13/2-3/2y solve for x in terms of y in the first equation
3(13/2-3/2y)-5y=-9 plug into the other equation
39/2-9/2y-10/2y=-18/2 distribute and set a common denominator
39/2-19/2y=-18/2
39-19y=-18 this is a matter of personal preference, but I like to multiply the whole equation by the denominator to get rid of fractions (for now)
-19y=-57
y=57/19
y=3

Now, going back to the other equation
2x+3(57/19)=13 plug in value of y
2x+171/19=13
2x+9=13
2x=4
x=2