Question 123074
3x+4y=7 
5x+2y=12


You need to find a way to eliminate one of the variables, by multiplying one or both of the equations by some number(s), and adding them together.  In this case, since you have a 4y and a 2y, if you want to make the 4y subtract out, you will need a -4y, so you should multiply the second equation by -2.


3x+4y=7
-10x-4y=-24


-7x = -17
{{{x= 17/7}}}


Since this came out to such an ugly answer, I would eliminate the x terms in the same way.  You have coefficients of x of 3 and 5.  A "common number" would be 15, so multiply the first equation by 5 and the second equation by -3, which will give you a 15x and -15x, which subtract out.


3x+4y=7
5x+2y=12


5(3x+4y)=5(7)
-3(5x+2y)=-3(12)


15x+20y = 35
-15x-6y=-36


14y=-1
y=-1/14


This is REALLY ugly, so check it by substituting into the first equation:
3x+4y=7
3(17/7) +4(-1/14) = 7
51/7 -2/7 = 7
49/7=7


Some instructors require a check in BOTH equations.  The second check will be similar to this!


R^2