Explanation:
4x + 3y = -10
9x + 2y = 6
we have 2 general options :
substitution or elimination.
in substitution we use one equation to express one variable by the other, then use that equality in the second equation and solve for the remaining variable.
like in our case
4x = -10 - 3y
x = (-10 - 3y)/4
in elimination we multiply one or both equations by some factors and then subtract one equation from the other resulting in one equation in one remaining variable.
this is the better method, if substitution leads to more complex fractions.
like in our case.
so, I would multiply equation 1 by 2 and equation 2 by 3, and then subtract e.g. equation 2 from 1 (we could also do it the other direction, it gives the same solutions) :
8x + 6y = -20
- 27x + 6y = 18
------------------------
-19x 0 = -38
-19x = -38
19x = 38
x = 2
and then we pick any of the original equations to get the other variable :
e.g.
4x + 3y = -10
4×2 + 3y = -10
8 + 3y = -10
3y = -18
y = -6