Question

Solve the system of equations

4x-8y=-36
-6x+y=32

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

First, let's solve the second equation for y:
-6x + y = 32
y = 6x + 32

Now, we can substitute this expression for y into the first equation:
4x - 8(6x + 32) = -36
4x - 48x - 256 = -36
-44x - 256 = -36
-44x = 220
x = -5

Now that we have found the value of x, we can substitute it back into the second equation to solve for y:
-6(-5) + y = 32
30 + y = 32
y = 2

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

Answer 2

Solve the system of equations.

6x-3y=-6
9x-3y=-18

Answer 3

[AI-generated answer — Bot GPT 3.5]

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

First, let's write the system of equations:
1. 6x - 3y = -6
2. 9x - 3y = -18

Now, we can subtract equation 1 from equation 2 to eliminate y:
(9x - 3y) - (6x - 3y) = -18 - (-6)
9x - 3y - 6x + 3y = -18 + 6
3x = -12
x = -4

Now that we have found the value of x, we can substitute it back into one of the equations to solve for y. Let's use equation 1:
6(-4) - 3y = -6
-24 - 3y = -6
-3y = 18
y = -6

Therefore, the solution to the system of equations is x = -4 and y = -6.

Answer 4

Solve the system of equations.

5x-4y=-44
-x+3y=22

Answer 5

[AI-generated answer — Bot GPT 3.5]

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

From the second equation, we can write it as:
-x + 3y = 22

Rearranging to solve for x:
x = 3y - 22

Now, substitute x into the first equation:
5(3y - 22) - 4y = -44
15y - 110 - 4y = -44
11y - 110 = -44
11y = 66
y = 6

Now that we have the value of y, we can substitute it back into x = 3y - 22:
x = 3(6) - 22
x = 18 - 22
x = -4

Therefore, the solution to the system of equations is x = -4 and y = 6.

Answer 6

-6x+2y=-32

4x+3y=-9

Answer 7

[AI-generated answer — Bot GPT 3.5]

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

We have the following equations:
1. -6x + 2y = -32
2. 4x + 3y = -9

To eliminate one of the variables, we will multiply equation 1 by 2 and equation 2 by 3 so that the y coefficients will be the same. This will allow us to eliminate y by subtraction.

Equation 1 multiplied by 2:
-12x + 4y = -64

Equation 2 multiplied by 3:
12x + 9y = -27

Now we will subtract the second equation from the first equation to eliminate y:
(-12x + 4y) - (12x + 9y) = -64 - (-27)
-12x + 4y - 12x - 9y = -64 + 27
-5y = -37
y = 7.4

Now that we have found the value of y, we can substitute it back into either of the original equations. Let's substitute it back into the first equation:
-6x + 2(7.4) = -32
-6x + 14.8 = -32
-6x = -46.8
x = 7.8

Therefore, the solution to the system of equations is x = 7.8 and y = 7.4.