Steven K. answered • 10/10/21
Harvard/Yale Grad with 25+ years teaching and tutoring
Set the equations on top of one another with variables and constants in the same respective positions, thus:
5x - 2y = 16
15x- 7y = 51
Figure out what number you have to multiply one of the equations by (say the top equation) so that one of the variables in that equation will have the same coefficient as that variable in the other equation. In this case, 3 will work. Multiply everything in the top equation by this factor (3 in this case) and rewrite both equations as before:
15x - 6y = 48
15x - 7y = 51
Now subtract every term in the bottom equation from the corresponding term in the top equation and solve:
15x-15x-6y-(-7y) = -3
y=-3 and plugging that solution back into either equation, x=2.
So the solution is (2,-3). Note that both equations here are lines, and this solution is the single point on the xy-plane at which they intersect.
