linear combinations are confusing, please show how to solve -6x + 5y = 4 and 7x - 10y = -8

Answer 1

we want 10 y in both so mutiply the whole first equation by 2

-12 x + 10 y = +8
+7 x - 10 y = -8
-----------------------add
- 5 x = 0
well, x = 0
then 5 y = 4
so
y = 4/5
or
-10 y = -8
so again y = 4/5 (that was a check)
the lines intersect at (0 , 4/5 )