-4x - 5y = 7
3x + 5y = -14
You can add these two equations together straightaway since the y-terms have opposite coefficients.
-4x - 5y = 7
3x + 5y = -14
+___________
-x - 0 = -7
-x = -7
x = 7
Substitute 7 for x into either of the original equations and solve algebraically to find y.
3x + 5y = -14
3(7) + 5y = -14
21 + 5y = -14
21 = -14 - 5y
35 = -5y
-7 = y
Finally, check work by substituting both x- and y-values into both original equations.
-4x - 5y = 7
-4(7) - 5(-7) = 7
-28 + 35 = 7
7 = 7
3x + 5y = -14
3(7) + 5(-7) = -14
21 - 35 = -14
-14 = -14
Answer:
x = 7 and y = -7; (7, -7).
