What is the solution to the system of equations?
-2x + y = -5
3x – 2y = 12
Responses
A (3, 1)(3, 1)
B (6, 3)(6, 3)
C (-2, -9)(-2, -9)
D (-2, -1)(-2, -1)
E no solution
To solve the system of equations, we can use the method of substitution or elimination.
We will use the method of elimination to solve this system.
First, let's multiply the first equation by 2 to eliminate the y term:
-4x + 2y = -10
Now, let's add this equation to the second equation:
(-4x + 2y) + (3x - 2y) = -10 + 12
Simplifying, we get:
-x = 2
To solve for x, we multiply both sides of the equation by -1:
x = -2
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y.
Let's use the first equation:
-2(-2) + y = -5
Simplifying:
4 + y = -5
Subtracting 4 from both sides:
y = -9
So the solution to the system of equations is (-2, -9).
Therefore, the correct answer is C. (-2, -9)