Question

What is the solution of the system? Use the elimination method. {4x+2y=66x−4y=−12

A.The solution is (32,0)


B.The solution is (0, 3) .


C.There are an infinite number of solutions.


D.There is no s

Answer 1

The Answer is B. The solution is (0,3).

Explanation:

I took the quiz and this was the answer.

Answer 2

`\begin{bmatrix}4x+2y=6\\ 6x-4y=-12\end{bmatrix}`


`\mathrm{Multiply\:}4x+2y=6\mathrm{\:by\:}3: 12x+6y=18`

`\mathrm{Multiply\:}6x-4y=-12\mathrm{\:by\:}2: 12x-8y=-24`


`\begin{bmatrix}12x+6y=18\\ 12x-8y=-24\end{bmatrix}`

12x - 8y = -24
-
12x + 6y = 18
/
-14y = -42


`\begin{bmatrix}12x+6y=18\\ -14y=-42\end{bmatrix}`


`Solve\;-14y=-42 \;for\;y \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-14 \ \textgreater \ (-14y)/(-14)=(-42)/(-14)`
y = 3


`\mathrm{For\:}12x+6y=18\mathrm{\:plug\:in\:} \:y=3`


`12x+6\cdot \:3=18 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:6\cdot \:3=18 \ \textgreater \ 12x+18=18`


`\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides} \ \textgreater \ 12x+18-18=18-18`


`\mathrm{Simplify} \ \textgreater \ 12x = 0 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}12 \ \textgreater \ (12x)/(12)=(0)/(12) \ \textgreater \ x = 0`


`Therefore\;the\:solutions\:are\;y=3,\:x=0`

Hope this helps!