Question

-3x-4y=-23
3x-5y=5

Answer 1

8X-6y=48
8X+6y=48
How many solutions does the system of equations have?

Answer 2

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

First, let's multiply the second equation by 3 to eliminate the x variable:

3(3x - 5y) = 3(5)
9x - 15y = 15

Now we have the system of equations:
-3x - 4y = -23
9x - 15y = 15

Next, add the two equations together to eliminate the x variable:
(-3x - 4y) + (9x - 15y) = -23 + 15
6x - 19y = -8

Now, we have the equation:
6x - 19y = -8

To find the value of y, we will solve for y by isolating it in the equation:
-19y = -8 - 6x
y = (-8 - 6x) / -19

Now, substitute y back into one of the original equations to solve for x. Let's use the first equation:
-3x - 4((-8 - 6x) / -19) = -23
-3x + 4(8 + 6x) / 19 = -23
-57x - 76 = -437
-57x = -361
x = 361 / 57
x = 5

Now that we have found x, we can substitute it back into either of the original equations to solve for y. Let's use the first equation:
-3(5) - 4y = -23
-15 - 4y = -23
-4y = -8
y = -8 / -4
y = 2

Therefore, the solution to the system of equations is x = 5 and y = 2.