Respuesta :
Answer:
x = 9 and y = -6.
Step-by-step explanation:
To find the solution of the given system of equations:
Equation 1: -3x + 2y = -39
Equation 2: 5x + 4y = 21
There are several methods to solve this system, such as substitution, elimination, or using matrices. Let's use the elimination method in this case:
To eliminate one variable, we need to multiply both equations by suitable coefficients so that the coefficients of either x or y become the same in both equations. In this case, let's eliminate the x variable by multiplying Equation 1 by 5 and Equation 2 by 3:
5 * (-3x + 2y) = 5 * (-39)
3 * (5x + 4y) = 3 * 21
Simplifying these equations, we get:
-15x + 10y = -195
15x + 12y = 63
Now, add these equations together to eliminate the x variable:
(-15x + 10y) + (15x + 12y) = -195 + 63
Simplifying further:
-15x + 15x + 10y + 12y = -132
Combining like terms:
22y = -132
Next, divide both sides of the equation by 22 to solve for y:
22y/22 = -132/22
Simplifying:
y = -6
Now substitute the value of y into one of the original equations, let's use Equation 1:
-3x + 2(-6) = -39
Simplifying:
-3x - 12 = -39
Add 12 to both sides:
-3x - 12 + 12 = -39 + 12
Simplifying further:
-3x = -27
Finally, divide both sides by -3 to solve for x:
-3x/-3 = -27/-3
Simplifying:
x = 9
Therefore, the solution to the system of equations is x = 9 and y = -6.
