Question

solve the system of equations.

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations:

We will use the method of substitution.

From the first equation, we can solve for x in terms of y:
6x - 3y = -6
6x = 3y - 6
x = (3y - 6)/6
x = (y - 2)/2

Now we substitute this value of x into the second equation:
9x - 3y = -18
9((y - 2)/2) - 3y = -18
(9y - 18)/2 - 3y = -18
(9y - 18 - 6y)/2 = -18
(3y - 18)/2 = -18
3y - 18 = -36
3y = -36 + 18
3y = -18
y = -18/3
y = -6

We substitute this value of y back into either equation to solve for x:
6x - 3(-6) = -6
6x + 18 = -6
6x = -6 - 18
6x = -24
x = -24/6
x = -4

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

Answer 2

solve the system of equations

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

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations:

We will use the method of substitution.

From the second equation, we can solve for x in terms of y:
-x + 3y = 22
x = 3y - 22

Now we substitute this value of x into the first equation:
5x - 4y = -44
5(3y - 22) - 4y = -44
15y - 110 - 4y = -44
11y - 110 = -44
11y = -44 + 110
11y = 66
y = 66/11
y = 6

We substitute this value of y back into the second equation to solve for x:
-x + 3(6) = 22
-x + 18 = 22
-x = 22 - 18
-x = 4
x = -4

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

Answer 4

[AI-generated answer — Explain Bot]

To solve this system of equations, you can use the method of substitution or elimination. Here, I will show you how to solve it using the method of elimination.

Step 1: Multiply both sides of the first equation by 3 to make the coefficients of y in both equations the same:
(3)(6x - 3y) = (3)(-6)
18x - 9y = -18

Step 2: Now, we can subtract the second equation from the modified first equation to eliminate the y term:
(18x - 9y) - (9x - 3y) = (-18) - (-18)
18x - 9y - 9x + 3y = -18 + 18
9x - 6y = 0

Step 3: Simplify the equation:
9x - 6y = 0
Divide both sides by 3:
3x - 2y = 0

Now we have a new equation: 3x - 2y = 0

Step 4: Solve for x or y by expressing one variable in terms of the other. Let's solve for x:
3x - 2y = 0
3x = 2y
x = (2y) / 3

Step 5: Now that we have the value of x in terms of y, substitute it back into one of the original equations to solve for y. Let's use the first equation:
6x - 3y = -6

Substitute the value of x:
6[(2y)/3] - 3y = -6
(12y/3) - 3y = -6
4y - 3y = -6
y = -6

Step 6: Substitute the value of y back into the equation to solve for x:
x = (2y) / 3
x = (2(-6)) / 3
x = -12 / 3
x = -4

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