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)?

Answer 1

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).

Answer 2

Are you sure? Double check please

Answer 3

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).

Answer 4

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)?

Answer 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).

Answer 6

Are you sure double check please?

Answer 7

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).