Question

3x-4y=6
5x-4y=2

Answer 1

3x-4y=6
5x-4y=2
Let's subtract the first equation from the second:
2x=-4 whence x=-2
Now we can find y. Consider the first equation:
3*(-2)-4y=6
4y=-6-6=-12 whence y=-3
So the answer is (-2,-3)

We can verify obtained answer by substituting it into initial system:
3*(-2)-4*(-3)=6& <=> -6+12=6& <=> 6=6
5*(-2)-4*(-3)=2& <=> -10+12=2& <=> 2=2

We obtained right equalities hence our answer is correct because it turns the initial system into right equalities.