Question

Solve the following system of equations.
-9x+8y=-13
-8x+3y=9

Answer 1

You sure?

Answer 2

Are you sure?

Answer 3

To solve this system of equations, we can use the method of substitution or elimination. Here, we will use substitution.

We are given the system of equations:
-9x + 8y = -13
-8x + 3y = 9

We will solve one of the equations for one variable and then substitute that expression into the other equation.

From the first equation:
8y = 9x - 13
y = (9/8)x - 13/8

Now we substitute y = (9/8)x - 13/8 into the second equation:

-8x + 3((9/8)x - 13/8) = 9
-8x + (27/8)x - 39/8 = 9
(1/8)x = 27/8
x = 27

Now, substitute x = 27 into y = (9/8)x - 13/8 to find y:

y = (9/8)(27) - 13/8
y = 81/2 - 13/8
y = 25/2

Therefore, the solution to the system of equations is x = 27 and y = 25/2.

Answer 4

Apologies for the mistake in the previous solution. Let's correct it.

Given equations:
-9x + 8y = -13
-8x + 3y = 9

Let's solve the system of equations using the elimination method.

Multiply the first equation by 3 and the second equation by 8 to make the coefficients of y equal:

-27x + 24y = -39
-64x + 24y = 72

Now, subtract the first equation from the second equation to eliminate y:

-64x + 24y - (-27x + 24y) = 72 - (-39)
-64x + 24y + 27x - 24y = 72 + 39
-37x = 111
x = -3

Now substitute x = -3 into either of the initial equations, I'll choose the first one:

-9(-3) + 8y = -13
27 + 8y = -13
8y = -40
y = -5

Therefore, the solution to the system of equations is x = -3 and y = -5.

Answer 5

Let's check the solution by substituting x = -3 and y = -5 back into the original equations:

1. -9x + 8y = -13
-9(-3) + 8(-5) = -13
27 - 40 = -13
-13 = -13

2. -8x + 3y = 9
-8(-3) + 3(-5) = 9
24 - 15 = 9
9 = 9

Since both equations hold true when x = -3 and y = -5, this confirms that the correct solution to the system of equations is x = -3 and y = -5.