Question
Solve the following system by the elimination method.
4x−2y=16
3x+6y=−18
(1 point)
Responses
(1, −5)
(1, −5)
(0, −3)
(0, −3)
(2, −4)
(2, −4)
(3, −2)
4x−2y=16
3x+6y=−18
(1 point)
Responses
(1, −5)
(1, −5)
(0, −3)
(0, −3)
(2, −4)
(2, −4)
(3, −2)
Answers
GPT 3.5
To solve the system by the elimination method, we need to eliminate one variable by multiplying one or both of the equations by a suitable number(s) so that the coefficients of one variable in both equations become the same or opposite.
In this case, let's eliminate the variable x by multiplying the first equation by 3 and the second equation by 4:
(3)(4x - 2y) = (3)(16)
(4)(3x + 6y) = (4)(-18)
This gives us:
12x - 6y = 48
12x + 24y = -72
Now, we can subtract the second equation from the first equation to eliminate x:
(12x - 6y) - (12x + 24y) = 48 - (-72)
12x - 6y - 12x - 24y = 48 + 72
-30y = 120
Dividing both sides by -30, we get:
y = -4
Substituting the value of y back into the first equation:
4x - 2(-4) = 16
4x + 8 = 16
4x = 8
x = 2
Therefore, the solution to the system is (2, -4), which matches with option (2, -4).
In this case, let's eliminate the variable x by multiplying the first equation by 3 and the second equation by 4:
(3)(4x - 2y) = (3)(16)
(4)(3x + 6y) = (4)(-18)
This gives us:
12x - 6y = 48
12x + 24y = -72
Now, we can subtract the second equation from the first equation to eliminate x:
(12x - 6y) - (12x + 24y) = 48 - (-72)
12x - 6y - 12x - 24y = 48 + 72
-30y = 120
Dividing both sides by -30, we get:
y = -4
Substituting the value of y back into the first equation:
4x - 2(-4) = 16
4x + 8 = 16
4x = 8
x = 2
Therefore, the solution to the system is (2, -4), which matches with option (2, -4).