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Choose the equivalent system of linear equations that will produce the same solution as the one given below.


6x + 2y = −6

3x − 4y = −18


12x + 4y = −12

15x = −30

8x + 4y = −4

14x = −10

6x − 8y = −36

−6y = −42

6x − y = −15

3y = 9

Verified Answer :

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The given system of equation:
\(6x+2y=-6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times 2 \\ 3x-4y=-18 \\ \\ 12x+4y=-12 \\ \underline{3x-4y=-18 \ \ } \\ 15x=-30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 15 \\ x=-2 \\ \\ 3x-4y=-18 \\ 3 \times (-2)-4y=-18 \\ -6-4y=-18 \ \ \ \ \ \ \ \ \ \ \ \ |+6 \\ -4y=-12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div (-4) \\ y=3 \\ \\ (x,y)=(-2,3)\)

Answer options:
1.
\(12x+4y=-12 \\ 15x=-30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 15 \\ \\ 12x+4y=-12 \\ x=-2 \\ \\ 12 \times (-2)+4y=-12 \\ -24+4y=-12 \ \ \ \ \ \ \ \ \ \ |+24 \\ 4y=12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 4 \\ y=3 \\ \\ (x,y)=(-2,3) \\ \hbox{the same solution}\)

2.
\(8x+4y=-4 \\ 14x=-10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 14 \\ \\ 8x+4y=-4 \\ x=-\frac{10}{14}=-\frac{5}{7} \\ \\ x=-\frac{5}{7} ot= -2 \\ \hbox{not the same solution}\)

3.
\(6x-8y=-36 \\ -6y=-42 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div (-6) \\ \\ 6x-8y=-36 \\ y=7 \\ \\ y=7 ot= 3 \\ \hbox{not the same solution}\)

4.
\(6x-y=-15 \\ 3y=9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 3 \\ \\ 6x-y=-15 \\ y=3 \\ \\ 6x-3=-15 \ \ \ \ \ \ \ \ \ |+3 \\ 6x=-12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 6 \\ x=-2 \\ \\ (x,y)=(-2,3) \\ \hbox{the same solution}\)

The equivalent systems of equations are 1 and 4:
12x+4y=-12
15x=-30
and
6x-y=-15
3y=9

Answer:12x+4y=-12

15x=-30

Step-by-step explanation:

just took the test and had to use the answer below to get it right but they got to answers :// thats dumb but theres the answer start forward

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