Multiplying the first equation by 6 and the second by 20 to get rid of fractions gives us:
(1) 3x - 2y = 5
(2) 4x - 5y = 30
We proceed by elimination. Multiplying equation (1) by 4 and equation (2) by 3 gives:
12x - 8y = 20
12x - 15y = 90.
Subtracting the bottom equation from the top one gives:
7y = -70.
Finally, dividing both sides by 7 gives y = -10.
To solve for x, we plug this value of y into (1), giving us:
3x - 2(-10) = 5.
Simplifying, we have
3x + 20 = 5.
Subtracting 20 from both sides, we have
3x = -15.
Finally, dividing both sides by 3 gives us:
x = -5.
Thus (x,y) = (-5,-10).
