Question

Select the best possible first step to solving the following system by first eliminating the y variable.
4x + 5y = -8
3x + 2y = 1

Answer 1

Multiply the first equation by 2 and multiply the second equation by 5.
Multiply the first equation by -2 and multiply the second equation by -5.
Multiply the first equation by -2 and multiply the second equation by 5.
Multiply the first equation by 8 and the second equation by -8.

Answer 2

Absolutely, positively, irrefutably, the VERY BEST possible first step is to read the problem statement.

Answer 3

What is the second step in eliminating a variable?
It is to add the 2 equations.
That means the first step must do something to the y-terms of the two equations, so that when you add them, the y-terms will be eliminated (add to zero).

Answer 4

Multiply the first equation by 2 and multiply the second equation by 5.
Multiply the first equation by -2 and multiply the second equation by -5.
Multiply the first equation by -2 and multiply the second equation by 5.
Multiply the first equation by 8 and the second equation by -8.

Answer 5

@tkhunny Technically speaking, I don't agree with you.
The first step in answering this question correctly is indeed to read the problem statement. That is true of any problem.
However, that is not what is being asked here. The question asked in the problem is already one step further. It is what is the first step in solving the system of equations, not what is the first step in answering this question correctly.

Answer 6

@jimmy142
Look at the two equations, but look only at the y-terms of the two equations.
They are 5y and 2y.
Now read each choice.
The correct choice is the one that tells you to multiply the first equation by a number and the second by another number, so that after you do the multiplications, the y-terms will add to zero.

Answer 7

Fair enough. I was being a little snarky before I realized the second post contained choices.

However, I'm going to defend my response a little because I find this language ridiculous: "the best possible first step" In my opinion, there should not EVER be used such language. The best possibly first step is whatever step the student understands and the step from which the student can learn how to approach similar problems.

Also technically, asking for a "first" step, and then providing possible choices that ALL include TWO steps is a little silly. I want the author of the problem statement to reconsider the actual goals of such a problem.

Answer 8

Each choice is a step that consists of two similar actions.
The step could be called "multiplying both equations by the appropriate factors."

Answer 9

Again, fair enough, but my personal outcomes became far, far more accurate when I stopped thinking like that. Each step - one piece at a time - methodical, reproducible, and accurate. The fact that we have disputed this point suggests even more strongly that the problem statement is horrible.

We are told to eliminate the y. We have to make the y-coefficients the same. Obviously, whichever double action accomplishes this is the intended answer. That doesn't justify the miserable construction of the problem statement.

Sorry, @jimmy142 - I've tried over the years to get students to THINK about what they are doing, rather than memorizing processes. This problem statement was written by someone who does not agree with my methods. I invite you to decide which camp you are in and either challenge your teacher/textbook or ignore me - whichever side of the fence you land.

Answer 10

how do i do your method

Answer 11

@tkhunny

Answer 12

For starters, you figure out how to get the question right. Society demands it! :-)

4x + 5y = -8
3x + 2y = 1

The plan is to add the two equations and have the y-variables disappear. What will accomplish that? As it stands, adding them:

7x + 7y = -7

The y-variables didn't go away.

The idea is to make the coefficients the same magnitude, but opposites signs. You will need a common multiple of 5 and 2 for that. In some cases, only one equation needs modification. Since 5 and 2 are mutually prime and neither is a multiple of the other, we have to go fishing. The least common multiple is 10. Which of the choices accomplishes this?

Answer 13

Multiply the first equation by 2 and multiply the second equation by 5.?

Answer 14

@tkhunny

Answer 15

Okay, let's do that:

8x + 10y = -16
15x + 10y = 5

Add them.

23x + 20y = -11

The y-variables didn't go away.

Make either the 5 or the 2 negative and we'll be there. If you pick -2, you will have discovered Choice #3. If you pick -5, you will have an equally valid response that is not included in the problem statement choices.

Answer 16

so none of the answers work?

Answer 17

@tkhunny

Answer 18

You missed this part:

If you pick -2, you will have discovered Choice #3.

Answer 19

ohhh

Answer 20

Whoops. I contradicted myself. I said both of these:

"We have to make the y-coefficients the same."
"The idea is to make the coefficients the same magnitude, but opposites signs."

The second is the more correct.

You can make them the SAME and then SUBTRACT, but I really don't like that. Making them OPPOSITE and then ADDING is far simpler and results in far fewer errors.

Answer 21

thanks! can you help me with another question?

Answer 22

Post a new thread.

@mathstudetn55 Sorry. It wasn't you at all. The question just told me I should get on my soapbox.