Question

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

Answer 1

Answer:12x+4y=-12

15x=-30

Explanation:

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Answer 2

The given system of equation:

`6x+2y=-6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |* 2 \\ 3x-4y=-18 \\ \\ 12x+4y=-12 \\ \underline{3x-4y=-18 \ \ } \\ 15x=-30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ 15 \\ x=-2 \\ \\ 3x-4y=-18 \\ 3 * (-2)-4y=-18 \\ -6-4y=-18 \ \ \ \ \ \ \ \ \ \ \ \ |+6 \\ -4y=-12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ (-4) \\ y=3 \\ \\ (x,y)=(-2,3)`

Answer options:
1.

`12x+4y=-12 \\ 15x=-30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ 15 \\ \\ 12x+4y=-12 \\ x=-2 \\ \\ 12 * (-2)+4y=-12 \\ -24+4y=-12 \ \ \ \ \ \ \ \ \ \ |+24 \\ 4y=12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ 4 \\ y=3 \\ \\ (x,y)=(-2,3) \\ \hbox{the same solution}`

2.

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

3.

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

4.

`6x-y=-15 \\ 3y=9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ 3 \\ \\ 6x-y=-15 \\ y=3 \\ \\ 6x-3=-15 \ \ \ \ \ \ \ \ \ |+3 \\ 6x=-12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ 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