Solve the system of equations

7x + 3y = -25

-7x + 9y = -47

1 answer

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

First, multiply the first equation by 7 and the second equation by -1 to eliminate x:

7(7x + 3y) = 7(-25)
-1(-7x + 9y) = -1(-47)

This simplifies to:
49x + 21y = -175
7x - 9y = 47

Now, add the two equations together to eliminate x:
49x + 21y + 7x - 9y = -175 + 47
56x + 12y = -128

Divide by 4 to simplify the equation:
14x + 3y = -32

Now we have a new equation:
14x + 3y = -32

We can now solve this new equation with one of the original equations:

7x + 3y = -25

Solving for y in terms of x, we get:
3y = -25 - 7x
y = (-25 - 7x) / 3

Now, substitute y into the new equation:
14x + 3((-25 - 7x) / 3) = -32
14x - 25 - 7x = -32
7x - 25 = -32
7x = -7
x = -1

Now that we have the value of x, we can substitute it back into the original equation to find y:

7(-1) + 3y = -25
-7 + 3y = -25
3y = -18
y = -6

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