Asked by sigma bsd

Solve the system of two equations using subtraction y equals 2 + 3x and 4x- 3y = -16, out of these answers, which one is correct? (2,8), (-2,-4), (-2,4) or (2,10)?
Answered by sigma bsd
Are you sure? Double check please
Answered by sigma bsd
Solve the system of equations. 2x + 6y = -18 and x = 5y- 1, which one of the following answers is correct? (5.25, 1.25), (-7.25, -1.25), (-6, -1) or (4, 1)?
Answered by sigma bsd
Are you sure double check please?
Answered by GPT 3.5
To solve the system of equations using subtraction, we need to first rewrite one of the equations so that the coefficients of either x or y are the same.

Let's rewrite the first equation, y = 2 + 3x, as 3x - y = -2.

Now we can subtract the two equations:

(4x - 3y) - (3x - y) = -16 - (-2)
4x - 3y - 3x + y = -16 + 2
x - 2y = -14

Now we have a new equation, x - 2y = -14, which represents the same relationship between x and y as the original system of equations. We can solve this equation along with the second equation, 4x - 3y = -16, using substitution or elimination.

Substituting x = -14 + 2y into the second equation, we get:

4(-14 + 2y) - 3y = -16
-56 + 8y - 3y = -16
5y = 40
y = 8

Substituting y = 8 back into the first equation, we get:

x = -14 + 2(8)
x = -14 + 16
x = 2

Therefore, the correct answer is (2, 8).
Answered by GPT 3.5
Apologies for the error in my previous response. Let's recheck the solution.

We have the system of equations:

y = 2 + 3x ...(1)
4x - 3y = -16 ...(2)

To solve using subtraction, let's first rewrite equation (1) in a different form. Subtracting 3x from both sides, we have 3x - y = -2.

Now, let's subtract equation (1) from equation (2):

(4x - 3y) - (3x - y) = -16 - (-2)
4x - 3y - 3x + y = -16 + 2
x - 2y = -14

So far, we have x - 2y = -14 as equation (3).

Now, we need to solve equations (2) and (3) simultaneously.

From equation (3), we can express x in terms of y:

x = -14 + 2y

Now substitute this value of x in equation (2):

4(-14 + 2y) - 3y = -16
-56 + 8y - 3y = -16
5y = 40
y = 8

Substituting y = 8 into equation (3), we have:

x - 2(8) = -14
x - 16 = -14
x = 2

Thus, the correct solution to the system of equations is (2, 8).
Answered by GPT 3.5
To solve the system of equations:

2x + 6y = -18 ...(1)
x = 5y - 1 ...(2)

Let's substitute equation (2) into equation (1):

2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1

Substituting y = -1 back into equation (2):

x = 5(-1) - 1
x = -5 - 1
x = -6

Therefore, the correct solution to the system of equations is (-6, -1).
Answered by GPT 3.5
Apologies for the error in my previous response. Let's recheck the solution.

We have the system of equations:

2x + 6y = -18 ...(1)
x = 5y - 1 ...(2)

To solve this system, let's substitute the value of x from equation (2) into equation (1):

2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1

Now, substitute the value of y = -1 back into equation (2) to find x:

x = 5(-1) - 1
x = -5 - 1
x = -6

Therefore, the correct solution to the system of equations is (-6, -1).