solve the system of equations

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

1 answer

To solve the system of equations, we can use the method of substitution or elimination. I will demonstrate solving it using the substitution method:

1) Solve one equation for one variable in terms of the other variable.

From the first equation, we can solve for x:

7x + 3y = -25

Move 3y to the other side:

7x = -25 - 3y

Divide by 7:

x = (-25 - 3y)/7

2) Substitute the value of x in the second equation.

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

Simplify:

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

25 + 3y + 9y = -47

Combine like terms:

25 + 12y = -47

3) Solve for y:

12y = -47 - 25

12y = -72

Divide by 12:

y = -6

4) Substitute the value of y back into either of the original equations to solve for x. Let's use the first equation:

7x + 3(-6) = -25

7x - 18 = -25

Add 18 to both sides:

7x = -25 + 18

7x = -7

Divide by 7:

x = -1

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