Question

Which ordered pair is the solution to the system of equations?

-3x+4y=-20
x+4y=-4

A.
(8, 1)

B.
(−12, 2)

C.
(−4, −8)

D.
(4, −2)

Answer 1

thank you
uh how do i start

Answer 2

are u there

Answer 3

(4, −2)

Answer 4

-3x+4y = -20--------(1)
x+4y = -4------------(2)


do subtraction (2) from (1)
u get the x value

Answer 5

@dayakar suggests a route to solve this called "elimination"
Another approach which would also be easy here is "substitution"

Take the second equation and solve it for one of the variables in terms of the other.
Here we have \[x + 4y = -4\]it is easy to solve that to get \(x\) in terms of \(y\):
\[x+4y - 4y = -4 - 4y\]\[x = -4 - 4y\]Now go to the first equation, and everywhere you see \(x\), replace it with \((-4-4y)\)

\[-3x+4y = -20\]\[-3(-4-4y) + 4y = -20\]\[12 + 12y + 4y = -20\]It should be easy to solve that for the value of \(y\). Once you know the value of \(y\), put that back into the substitution equation \[x =-4-4y\]to get your value for \(x\). The solution will be \((x,y)\)

Another approach, useful for checking your work, is to plug your answer (or proposed answer) into both equations and make certain that the equations produced are true, rejecting all choices that do not make both equations true. This is a necessary and sufficient test of your solution's correctness, because only a correct solution will make them all true. It is possible to get a "solution" which only works for one of the equations. Be careful that you don't fall into this trap. There is a technical term for such solutions: "wrong" :-) And the author of this problem has put in at least one answer choice that works for only one of the equations, no doubt to catch those who are not sufficiently diligent.