Solve the system of equations.

Question

7x+3y=−25

−7x+9y=−47

Answer 1

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

First, let's multiply the first equation by 7 and the second equation by -7 in order to eliminate the x-term:

(7)(7x + 3y) = (7)(-25)
(7)(-7x + 9y) = (7)(-47)

Simplifying these equations, we get:
49x + 21y = -175
-49x - 63y = -329

Adding these two equations together, we eliminate the x-term:
49x + 21y + (-49x - 63y) = -175 + (-329)
49x - 49x + 21y - 63y = -175 - 329
-42y = -504

Dividing both sides by -42, we solve for y:
y = (-504) / (-42)
y = 12

Now, we substitute this value of y back into one of the original equations to solve for x. Let's use the first equation:
7x + 3(12) = -25
7x + 36 = -25
7x = -25 - 36
7x = -61
x = -61 / 7
x = -8.71 (rounded to two decimal places)

Therefore, the solution to the system of equations is x = -8.71 and y = 12.