find the values of x and y that solve the following system of equations
3x+2y=-22
5x -9y=25
To solve the system of equations:
1. Let's start by choosing one equation to eliminate one of the variables. In this case, let's eliminate the variable x.
2. Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations the same.
5(3x + 2y) = 5(-22) (multiply the first equation by 5)
3(5x - 9y) = 3(25) (multiply the second equation by 3)
Simplifying these equations, we get:
15x + 10y = -110
15x - 27y = 75
3. Now, subtract the second equation from the first equation to eliminate the variable x.
(15x + 10y) - (15x - 27y) = -110 - 75
Simplifying, we get:
37y = -185
4. Divide both sides of the equation by 37 to solve for y:
y = -185/37
Simplifying, we find that y = -5.
5. Now, substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
3x + 2(-5) = -22
Simplifying this equation gives:
3x - 10 = -22
6. Add 10 to both sides of the equation:
3x = -12
7. Divide both sides of the equation by 3:
x = -12/3
Simplifying, we find that x = -4.
Therefore, the solution to the system of equations is x = -4 and y = -5.