-5x + 7y = 67

Question

11x + 12y = 17

What is the solution for the system of equations above?

Answer 1

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the method of substitution:

From the first equation, we can solve for x in terms of y:
-5x + 7y = 67
-5x = -7y + 67
x = (7y - 67)/5

Now, we substitute this expression for x into the second equation:
11x + 12y = 17
11((7y - 67)/5) + 12y = 17
(77y - 737)/5 + 12y = 17
77y - 737 + 60y = 85
137y - 737 = 85
137y = 822
y = 822/137
y = 6

Substituting y = 6 into the expression for x:
x = (7(6) - 67)/5
x = (42 - 67)/5
x = -25/5
x = -5

Therefore, the solution for the system of equations is x = -5 and y = 6.