Question

6x-5y=27

3x+5y=36

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can use the method of elimination. Adding the two equations together will allow us to eliminate the variable y:

(6x - 5y) + (3x + 5y) = 27 + 36
9x = 63
x = 7

Now that we have found the value of x, we can substitute it back into either of the original equations to solve for y. Let's substitute x = 7 into the first equation:

6(7) - 5y = 27
42 - 5y = 27
-5y = -15
y = 3

Therefore, the solution to the system of equations is x = 7 and y = 3.

Answer 2

2x+8y=8

2x-4y=-6

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can use the method of elimination as well. By subtracting the second equation from the first equation, we can eliminate the variable x:

(2x + 8y) - (2x - 4y) = 8 - (-6)
12y = 14
y = 7/6

Now that we have found the value of y, we can substitute it back into either of the original equations to solve for x. Let's substitute y = 7/6 into the first equation:

2x + 8(7/6) = 8
2x + 56/6 = 8
2x + 28/3 = 8
2x = 8 - 28/3
2x = 24/3 - 28/3
2x = -4/3
x = -2/3

Therefore, the solution to the system of equations is x = -2/3 and y = 7/6.

Answer 4

That was supposed to be -16 my bad

Answer 5

[AI-generated answer — Bot GPT 3.5]

No problem! Let's correct the mistake and work on the system of equations again:

2x + 8y = 8
2x - 4y = -16

Now, we will again use the method of elimination to solve this system of equations. By adding the two equations together, we can eliminate the variable x:

(2x + 8y) + (2x - 4y) = 8 + (-16)
12y = -8
y = -2/3

Now that we have found the value of y, we can substitute it back into either of the original equations to solve for x. Let's substitute y = -2/3 into the first equation:

2x + 8(-2/3) = 8
2x - 16/3 = 8
2x = 8 + 16/3
2x = 24/3 + 16/3
2x = 40/3
x = 20/3

Therefore, the solution to the modified system of equations is x = 20/3 and y = -2/3.