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)?
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).
Are you sure? Double check please
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).
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)?
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).
Are you sure double check please?
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).