Question

Solve
-6x+2y=-32
4x+3y=-9

Answer 1

Is that the correct answer

Answer 2

To solve this system of equations, we can use the method of elimination.

First, we will multiply the first equation by 2 to make the coefficients of y the same in both equations:

-12x + 4y = -64

Next, we will add this new equation to the second equation to eliminate y:

-12x + 4y = -64
4x + 3y = -9
______________
-8x = -73
________
-19/-8 = x
19/8 = x

Now that we have found 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:

-6(19/8) + 2y = -32
-57/4 + 2y = -32
2y = -32 + 57/4
y = -64/2 + 57/8
y = -128/8 + 57/8
y = -71/8

Therefore, the solution to the system of equations is x = 19/8 and y = -71/8.

Answer 3

I apologize for the error in my previous response. Let's correct the solution:

Given equations:
-6x + 2y = -32
4x + 3y = -9

Let's solve this system of equations using the method of elimination:

1. Multiply the first equation by 2 to make the coefficients of y the same in both equations:
-12x + 4y = -64

2. Add this new equation to the second equation to eliminate y:
-12x + 4y + 4x + 3y = -64 - 9
-8x + 7y = -73

Now we have a new equation:
-8x + 7y = -73

3. Solve this equation simultaneously with the second equation:
4x + 3y = -9

Let's multiply the second equation by 8:
32x + 24y = -72

Now, we will multiply the first equation by 4:
-32x + 28y = -292

4. Add the two new equations to eliminate x:
-32x + 28y + 32x + 24y = -292 - 72
52y = -364
y = -364 / 52
y = -7

5. Substitute y = -7 back into the second equation to find x:
4x + 3(-7) = -9
4x - 21 = -9
4x = -9 + 21
4x = 12
x = 12 / 4
x = 3

Therefore, the correct solution to the system of equations is x = 3 and y = -7. Thank you for pointing out the error, and I appreciate your patience.