Question

how many solutions does these equations have

x + y = -7

-2x -2y =14

Answer 1

[AI-generated answer — Bot GPT 3.5]

These two equations have one solution.

Answer 2

you sure

Answer 3

[AI-generated answer — Bot GPT 3.5]

Yes, I am sure. Let's solve the system of equations to verify:

1) x + y = -7
2) -2x - 2y = 14

Let's start by multiplying the first equation by 2 to make the coefficients of y the same:

1) 2x + 2y = -14
2) -2x - 2y = 14

Adding these two equations together:
(2x + 2y) + (-2x -2y) = -14 + 14
0 = 0

This means that the system of equations is consistent and dependent and has infinitely many solutions. I apologize for my previous incorrect response.

Answer 4

solve these equations by elimination

12x - 10y =2
-6x + 7y = -11

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations by elimination, we need to manipulate the equations so that when added or subtracted, one variable is eliminated.

1) 12x - 10y = 2
2) -6x +7y = -11

To eliminate the variable y, we can multiply the second equation by 5:

1) 12x - 10y = 2
2) -30x + 35y = -55

Now, if we add these two equations together, we can eliminate y:

12x - 10y -30x + 35y = 2 - 55
-18x + 25y = -53

Now, we can solve this new equation to find the value of x:

25y = 18x - 53
y = (18x - 53)/25

Now, substitute this expression for y back into one of the original equations to solve for x:

12x - 10(18x - 53)/25 = 2
12x - 180x/25 + 530/25 = 2
(300 - 180x + 530)/25 = 2
(830 - 180x)/25 = 2
830 - 180x = 50
-180x = -780
x = 4.33 (rounded to two decimal places)

Now, substitute x back into one of the original equations to solve for y:

12(4.33) - 10y = 2
51.96 - 10y = 2
-10y = -49.96
y = 4.99 (rounded to two decimal places)

Therefore, the solutions to the system of equations are x ≈ 4.33 and y ≈ 4.99.

Answer 6

ACTUAL ANSWER PLS

Answer 7

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake in my calculations. Let's re-calculate the system of equations using elimination:

1) 12x - 10y = 2
2) -6x + 7y = -11

To eliminate y, we can multiply the first equation by 7 and the second equation by 10:

1) 84x - 70y = 14
2) -60x + 70y = -110

Now, add the two equations together to eliminate y:

84x -70y - 60x + 70y = 14 - 110
24x = -96
x = -4

Now, substitute x back into the first equation to solve for y:

12(-4) - 10y = 2
-48 - 10y = 2
-10y = 50
y = -5

Therefore, the solution to the system of equations is x = -4 and y = -5.