Hi this question I am not sure about, I am debating so may you please help me confirm the correct answer (Algebra)

- help_people

- jamiebookeater

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- help_people

The table below shows four systems of equations:
System 1
System 2
System 3
System 4
4x − 5y = 2
3x − y = 8
4x − 5y = 2
10x − 7y = 18
4x − 5y = 2
3x − 8y = 4
4x − 5y = 2
10x + 3y = 15
Which pair of systems will have the same solution?
System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1
System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to two times the second equation in system 2
System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to three times the second equation in system 1
System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to three times the second equation in system 2

- help_people

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## More answers

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- anonymous

15

- help_people

- anonymous

hi

- help_people

- help_people

hi 04

- help_people

i am not sure may you walk me through the process?

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- mathstudent55

Every system has the same equation:
4x - 5y = 2

- mathstudent55

We need to look at the second equation of the 4 systems and compare them.

- mathstudent55

4x − 5y = 2
3x − y = 8
4x − 5y = 2
10x − 7y = 18
4x − 5y = 2
3x − 8y = 4
4x − 5y = 2
10x + 3y = 15

- help_people

well that have 10 x and 3x?

- help_people

but all different ys?

- mathstudent55

Look at choice A.
Choice A tells you that the second equation of the second system is 2 times the second equation of the first system added to the first equation of the first system. If this is true, the equations are the same equation and the solutions will be the same.
All you need to do is see if this is true.
Multiply the second eq. of system 1 by 2.
Then add it to the first eq. of system 1.
What do you get?

- help_people

who do i do that

- help_people

like 12-6y=16

- mathstudent55

Here is eq. 2 of system 1:
3x − y = 8
Multiply both sides of the equation by 2. What do you get?

- mathstudent55

Multiply both sides by 2:
2(3x − y) = 2(8)
What do you get?

- help_people

6x-2y=16

- mathstudent55

Great.
Now add it to the first eq. of system 1.
4x - 5y = 2
(+) 6x - 2y =16
-----------------
What do you get?

- help_people

10x+7y=18 @mathstudent55

- mathstudent55

Check the +7y.
Notice you are adding -5y and -2y.
What is -5y + (-2y) = ?

- help_people

-7y

- mathstudent55

-5y + (-2y) = -5y - 2y = -7y
Correct.

- mathstudent55

The equation is: 10x - 7y = 18
Now compare this new equation with the second eq. of system, 2.

- help_people

ok so what would i do? can you walk me through with it? @mathstudent55

- mathstudent55

The equation you got by doing what choice A tells you is exactly the second eq. of system 2. That means the answer is choice A. The first and second systems have the same answer.

- help_people

thank you so much may you help me w. more (its about squre roots)

- mathstudent55

Sorry, but I have to go.

- mathstudent55

You're welcome.

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