Question

MEDAL AND FAN! PLZ HELP
Two systems of equations are shown below:
System A:
6x+y=2
-x-y=-3
System B:
2x-3y=-10
-x-y=-3
Which of the following statements is correct about the two system equations?

Answer 1

A) The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A.
B) They will have the same solution because the first equations of both the systems have the same graph.
C) They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.
D) The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding -4 to the first equation of System A and the second equations are identical.

Answer 2

@SolomonZelman I have no idea how to do this can you help me?

Answer 3

I think we first have to solve each of the systems, don't we?

Answer 4

Alright how do I solve a system :( Could you walk me through one?

Answer 5

Lets start from system A,
\(\large\color{black}{ 6x~~~+y=~~~2 \\ -x~-y=~-3}\)

Answer 6

I would suggest to add the equations.

Answer 7

so like 6x-x+y-y-3=2?

Answer 8

than it would be 5x-3=2?

Answer 9

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

Answer 10

add the 3 on both sides?

Answer 11

oh

Answer 12

add all of the aXes, all the whYs all the numbers that are on the right sides together.

Answer 13

so 5x=-1?

Answer 14

yes.

Answer 15

So, what is x equal to?

Answer 16

x=-1/5?

Answer 17

yes.

Answer 18

now that you know that x=-1/5 can you solve for y?

Answer 19

reminding the system is,
\(\large\color{black}{ 6x~~~+y=~~~2 \\ -x~-y=~-3}\)

( you can use my latex `\(\large\color{black}{ 6x~~~+y=~~~2 \\ -x~-y=~-3}\)` )

Answer 20

y=0?

Answer 21

not really, no.

Answer 22

6y=-1?

Answer 23

sorry,
\(\large\color{black}{ 6(-\frac{1}{5})~~~+y=~~~2 \\ -(-\frac{1}{5})~-y=~-3}\)

if you get the same result for y, in both of the systems, that will also verify the solution.

Answer 24

\(\large\color{black}{ 6(-\frac{1}{5})~~~+y=~~~2 \\ -(-\frac{1}{5})~-y=~-3}\)



\(\large\color{black}{ -6\frac{1}{5}~~~+y=~~~2 \\ \frac{1}{5}~-y=~-3}\)

Answer 25

double negatives mean positive so 6(-1/5) +(1/5) so it would still be 6(1/5)

Answer 26

wait, I maid a mistake again.

Answer 27

no, I didn't.

Answer 28

sorry for confusing.

Answer 29

No no its fine I'm here to learn ^_^

Answer 30

\(\large\color{black}{ -6\frac{1}{5}~~~+y \color{red}{+6\frac{1}{5}}=~~~2\color{red}{+6\frac{1}{5}} \\ \frac{1}{5}~-y\color{red}{-\frac{1}{5}}=~-3\color{red}{-\frac{1}{5}}}\)

Answer 31

see what I am doing?

Answer 32

Yes your adding 6(1/5) to the top numbers and subtracting (1/5) from the bottom numbers

Answer 33

yes, which isolates the y in both of the equations:)

Answer 34

what do you get for y?

Answer 35

For the top equation I got y=8(1/5)
For the bottom equation I got -y=-3(1/5)

Answer 36

yes, I am not sure what do really do here, I went over the work we did:

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

\(\large\color{black}{ 5x=-1}\)

Answer 37

and then x=-1/5.

Answer 38

@Loser66 maybe you see the mistake?

Answer 39

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

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

\(\large\color{black}{-5y=-16}\)

\(\large\color{black}{ y=5/16}\)