Question

Solve the system of equations
7x+3y=-25
-7x+9y=-47

Answer 1

To solve this system of equations, we can use the method of substitution or the method of elimination. Since the coefficients of x in both equations are opposites, we can utilize the method of elimination.

By adding the two equations together, the x terms cancel out:

(7x + 3y) + (-7x + 9y) = (-25) + (-47)
3y + 9y = -72
12y = -72
y = -72/12
y = -6

Now we can substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:

7x + 3(-6) = -25
7x - 18 = -25
7x = -25 + 18
7x = -7
x = -7/7
x = -1

Therefore, the solution to the system of equations is x = -1 and y = -6.