Solve the system of equations. 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 9 and the second equation by 3 to eliminate the variable x:

(9)(7x+3y) = (9)(-25) -> 63x + 27y = -225
(3)(-7x+9y) = (3)(-47) -> -21x + 27y = -141

Now, subtract the second equation from the first equation to eliminate the variable y:

(63x + 27y) - (-21x + 27y) = -225 - (-141)
63x + 27y + 21x - 27y = -225 + 141
84x = -84
x = -84/84
x = -1

Substitute the value of x = -1 back into the first equation to solve for y:

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

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