So we have to solve 5x + 7y = 10, -3x + 14y = -6 by substitution, and we do this by, you guessed it, substituting!
5x + 7y = 10 --We first have to get x = something, so we can substitute x to find y.
/5 /5 /5 --Divide everything by 5
x + 7/5y = 2
-7/5y -7/5y --Subtract 7/5y from both sides
x = -7/5y + 2
-3x + 14y = -6
-3(-7/5y + 2) + 14y = -6 --Substitute x in
21/5y -6 + 14y = -6
+6 +6
4 1/5y + 14y = 0
y = 0
5x + 7(0) = 10 --Now put in y to find x
5x = 10
x = 2
So y = 0 and x = 2.
Let's check it:
-3(2) + 14(0) = -6
-6 = -6 ✔
