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

Answer 1

Answers:



12x + 4y = -12
15x = -30

8x + 4y = -4
14x = -10

6x - 8y = -36
-6y = -42

6x - y = -15
3y = 9

Answer 2

solve each of the 4 options for x and y and see if they fit the equations in the question

for example for first option
x = -30/15 = -2

now find y by plugging x=-2 in first equation

and see if the results fit

Answer 3

OKay well im still a little confused.. IM not to sure how to solve these in the first place.. could you walk me through one?

Answer 4

I'll find y for you in the first option:
12x + 4y = -12
now we found x = -2 so
12(-2) + 4y = -12
4y = -12 + 24 = 12
y = 12/4 = 3

Answer 5

now replace x by -2 and y by 3 in the equations in your question and see if they fit

Answer 6

Wait wait.. How do you know x = -2?

Answer 7

look at my first post

Answer 8

15x = -30
so x = -2

Answer 9

Oh okay i see..

Answer 10

so try the first equation in the question
6x + 2y = -6
x=-2, y=3 so we have
6(-2) + 2(3) = -12 + 6 = -6

so that one fits
now try the same values in the second equation:
3x - 4y = -18

Answer 11

if they fit then you have your answer

Answer 12

This is what you said:
I'll find y for you in the first option:
12x + 4y = -12
now we found x = -2 so
12(-2) + 4y = -12
4y = -12 + 24 = 12
y = 12/4 = 3

So i understand that you plug in -2 into x so you would get 12(-2) + 4y = -12

But then in the next step i kinda got confused again.. 4y = -12 + 24 = 12 so you what did you exactly do? So would you do? Did you multiply 12 by -2?

Answer 13

What did you do to get 4y all by itself on one side of the equation?

Answer 14

12(-2) + 4y = -12
-24 + 4y = -12
add 24 to both sides of the equation
-24 + 24 + 4y = -12 + 24
4y = -12+24 = 12
now divide both sides by 4
y = 3

Answer 15

\(\large\color{black}{ 6x + 2y = -6 \\
3x - 4y = -18 }\)

2nd equation times -2.

\(\large\color{black}{ 6x + 2y = -6 \\
-6x +8y = 36 }\)

and the equations and tell me what you get for y.

Answer 16

12(-2) + 4y = -12
-24 + 4y = -12
add 24 to both sides of the equation
-24 + 24 + 4y = -12 + 24
4y = -12+24 = 12
now divide both sides by 4
y = 3

Okay i understand everything up until 4y = -12+24 = 12

I so understand how 4y = -12+24 got there but where did the = 12 come from?

Answer 17

@cwrw238

Answer 18

@cwrw238 will cross mutiplication method be helpful??

Answer 19

Oh wait im so dumb... -12 + 24 = 12....

Answer 20

So then you would be left with 4y = 12 then you said to divide both sides so x = 3

Answer 21

yes

Answer 22

Okay thank you so much xD youre so helpful !!!!

Answer 23

yw

Answer 24

Wait before you go.. I have one more question.... the equation
8x + 4y = -4
14x = -10

Would you divide 10 by 14 to find out what x equals?

Answer 25

@SolomonZelman