Question

What is the value of the x variable in the solution to the following system of equations?

2x − 3y = 3
5x − 4y = 4

−1
zero
x can be any number as there are infinitely many solutions to this system
There is no x value as there is no solution to this system

Answer 1

have u ever heard of the matrix theorem?

Answer 2

also…couldn't you solve by elimination? which are you familiar with? @Niall ?

Answer 3

it think u can do both but ive came to know matrix theorem is a lot easier its just more steps

Answer 4

Since you only want the x value, eliminate the y variable and solve for x.
Multiply the first equation by -4.
Multiply the second equation by 3.
Then add the two equations together.
The y variable will be eliminated, and you'll have a single equation with only x that you can solve for x.

Answer 5

niall what do u prefer?

Answer 6

No, I haven't heard of the matrix theorem, and yeah, I'm familiar with the elimination method

Answer 7

I prefer the one thats easier :P

Answer 8

@mathstudent55

The first step is this, right?

*-4: 2x − 3y = 3
-8x + 12y = -12

Answer 9

Why don't you try elimination as I explained above.
Can you multiply the first equation by -4 and show what you get?

Answer 10

Yes, correct.

Answer 11

Now multiply the second equation by 3.

Answer 12

5x − 4y = 4

15x - 12y = 12

Answer 13

Great.
Using the new multiplied equations, now write the first equation and the second equation just below it, lining up the variables. Notice that the y variable terms are 12y and -12y which add to zero.

Answer 14

Now add the equations

-8x + 12y = -12
(+) 15x - 12y = 12
-------------------------

Answer 15

So would the final answer be 7?

Answer 16

We're solving it together. Let's continue. Now add the equations together. I already set it up for you above.

Answer 17

-8 + 15 = 7x

+12 + -12 = 0[x]

And again, +12 + -12 = 0

Answer 18

-8x + 12y = -12
(+) 15x - 12y = 12
-------------------------
7x = 0

Answer 19

You need to keep the variables.

Answer 20

Now you have a simple equation in only x, so you can solve it.

Answer 21

7x = 0

Divide both sides by 7:

x = 0

Answer 22

So 0's the value of the x variable?

Answer 23

Correct. In this system, x = 0.

Answer 24

That is one of the choices.

Answer 25

Ok, thanks a ton!!!! I like it way better when people actually take the time to explain how to find the answer, than when they just give it to you! =D

Answer 26

Can you explain how to solve this too, please?

The three Math Idol judges have been eliminating contestants all day! The number of one-step equations and two-step equations who have been eliminated today is equal to 1070! If three times the number of one-step equations minus twice the number of two-step equations is equal to 110, how many one-step equations auditioned today?

900
620
520
450

Answer 27

Let's call the number of one-step equations x
and the number of two-step equations y.

Answer 28

The total number of one-step and two-step equations is 1070.
Can you use x and y to write the above statement as an equation?

Answer 29

Um x + y = 1070?

Answer 30

Great.

Answer 31

Now we need to use again x and y to translate the other statement into an equation.

Answer 32

"If three times the number of one-step equations minus twice the number of two-step equations is equal to 110"

We need to write the above statement as an equation.

Answer 33

Ok, so: 3x - 2y = 110?

Answer 34

three times the number of one-step equations ---> 3x
twice the number of two-step ---> 2y

Answer 35

Great. You're ahead of me.

Answer 36

Now we have a system of two equations in two unknowns.

x + y = 1070
3x - 2y = 110

Answer 37

Notice the question is "how many one-step equations auditioned today?"

Since we let x represent one-step equations, we only need to solve for x.

Answer 38

Adding the equations together as they are will not help because it will not eliminate any variable. We want to eliminate y since we are only interested in x.

If we add y (of the first equation) and -2y (of the second equation) together, we get -y. We want zero y, not -y.

Answer 39

Ohh I see

Answer 40

All we need to do is to multiply the first equation by 2. This way the y term of the first equation will be 2y, which when added to the -2y of the second equation will give us zero y and will eliminate the y variable.

Answer 41

Now we multiply the first equation by 2 and write the second equation below.

Answer 42

So 2x + 2y = 2140
--------------
3x - 2y = 110

Answer 43

x + y = 1070 ---- (times 2) ----> 2x + 2y = 2140
3x - 2y = 110 ---- (just copy) ----> 3x - 2y = 110
(add)--------------
5x = 2250

Answer 44

Yes, you are correct. Now you add the equations you wrote.

Answer 45

So then you would divide 2250 by 5? :)

Answer 46

Right. Since we ended up with 5x = 225, we divide both sides by 5 to find x.
On the right side, that means divide 2250 by 5.

Answer 47

x = 450

Answer 48

Correct.

Answer 49

Okay! Thank you sooooo much!!! =D I really appreciate the help!

Answer 50

Since x represents the number of one-step equations the answer is
"450 one-step equations"

Answer 51

You're welcome.