find the values of x and y that solve te following system of equations

3x+2y=-22
5x-9y=25

first one times 9 ---> 27x + 18y = - 198

2nd one times 2 ---> 10x - 18y = 50

add them : 37x = -148
x = -4

I will let you finish it.

3x+2y=-22 (1)

5x-9y=25 (2)
Multiply (1) by 9 and (2) by 2 to get the y's to cancel
27x+18y=-198 (3)
10x-18y=50 (4)
Add (3) and (4) together
37x=-148
Divide both sides by 37
x=-4
Substitute that in either original equation (1) or (2) to solve for y. Check to make sure it works for the other equation, as well.

To find the values of x and y that solve the system of equations, we can use the method of substitution or the method of elimination. I will explain both methods, and you can choose the one you prefer.

Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for x:
3x + 2y = -22
3x = -2y - 22
x = (-2y - 22)/3

Step 2: Substitute the expression we found for x into the other equation.
Now, substitute the expression (-2y - 22)/3 for x in the second equation:
5x - 9y = 25
5((-2y - 22)/3) - 9y = 25

Step 3: Simplify and solve for y.
Multiply through by 3 to get rid of the fraction:
5(-2y - 22) - 27y = 75
-10y - 110 - 27y = 75
-37y - 110 = 75
-37y = 75 + 110
-37y = 185
y = 185/(-37)
y = -5

Step 4: Substitute the value of y back into the equation we found for x to get the value of x.
Substitute y = -5 into x = (-2y - 22)/3:
x = (-2(-5) - 22)/3
x = (10 - 22)/3
x = -12/3
x = -4

Therefore, the solution to the system of equations is x = -4 and y = -5.

Method 2: Elimination
Step 1: Multiply one or both equations by constant(s) so that the coefficients of one of the variables in the two equations are additive inverses (i.e., their sum is zero).
Let's multiply the first equation by 5 and the second equation by 3 to make the coefficients of x additive inverses:
15x + 10y = -110 (Equation 1)
15x - 27y = 75 (Equation 2)

Step 2: Add the two equations together to eliminate x.
(15x + 10y) + (15x - 27y) = -110 + 75
30x - 17y = -35

Step 3: Solve the resulting equation for y.
30x - 17y = -35
-17y = -30x - 35
y = (-30x - 35)/(-17)

Step 4: Substitute the found value for y into one of the original equations to find x.
Substitute the expression (-30x - 35)/(-17) for y in the first equation:
3x + 2((-30x - 35)/(-17)) = -22

Now, solve this equation for x.

Once you find the value of x, substitute it back into either of the original equations to find the value of y.

Please let me know if you want me to calculate it for you using a specific method or if you have any further questions!