Question

Someone explain this please? :/

Answer 1

Choose the equivalent system of linear equations that will produce the same solution as the one given below.

4x - y = -11
2x + 3y = 5

-4x - 9y = -19
-10y = -30

4x + 3y = 5
2y = -6

7x - 3y = -11
9x = -6

12x - 3y = -33
14x = -28

Answer 2

I'm confused as to how to go about this.

Answer 3

you could try solving for each system of equations and see which one matches up

Answer 4

remember the substitution method

Answer 5

I had been trying the elimination method o.o

Answer 6

How do I know when to use which method?

Answer 7

I have trouble reading the question itself, like which one is the given 'original' set of equations. However it does not matter for my explanation.

Two sets of linear equations definitely have the same solution set if they are equivalent, meaning the same, so for your equations above you could check if you can transform your original system of equations by scalar multiplication into one given in your list.

Answer 8

If this does not help with your question, you might want to rewrite it, showing us which is the 'original' set of equations and which are your alternative choices that you need to check whether or not they have the same solution set.

Answer 9

the original is the first one, the ones after it are my choices

Answer 10

Choose the equivalent system of linear equations that will produce the same solution as the one given below.
4x - y = -11 2x + 3y = 5

-4x - 9y = -19 | -10y = -30
4x + 3y = 5 | 2y = -6
7x - 3y = -11 | 9x = -6
12x - 3y = -33 | 14x = -28

Answer 11

Does that work?

Answer 12

I see that now, apparently they have 'disguised' the sets of equations already, meaning that they partially solved it (elimination).

Frankly said I believe that in this way the best approach would be to solve your original set of equations for \(x,y\) which will certainly have an unique solution. Then as suggested above, check with the remaining systems of equations if their solution set is equivalent.

Sounds like a big deal? Not really, solving your original system is a basic thing to do, then you want to notice that for all the 2x2 systems below you immediately know one answer already.

In the first choice lets call it 1 you know y already (by the 2nd equation)
2 you know y already (by the 2nd equation)
3 you know x already (by the 2nd equation)
4 you know x already (by the 2nd equation)

Answer 13

I am not sure what you're trying to do, have you tried to follow my hint?
First solve the following system of equations \[4x - y = -11 \\
2x + 3y = 5 \]
It will give you an unique \(x\) and a unique \(y\). For all the remaining systems of equations below you can immediately read AT LEAST one solution \(x\) or \(y\). Look closely at the alternative systems of equations, the 2nd lines always throw a solution right at you.

Do a comparison and you are done

Answer 14

right!!! 12x - 3y = -33
14x = -28 has the same solution!

Answer 15

Thanks!

Answer 16

you're welcome :)

Answer 17

still here