Question

*I'll help you in Psych, English, and Philosophy in return

Use the substitution method to solve the following system of equations.x + y = 32x + 2y = 10




(1, 2)

(2, 3)

No Solutions

Infinitely Many Solutions

Answer 1

Incorrect

Answer 2

Something funny is going on with these questions. Are you sure you're putting down the equations correctly?

Answer 3

You're basically saying there is no solution, which I can see

Answer 4

Yes, I'm 100% sure. I don't see how a professor would put out questions that aren't set up correctly, but you know...

Answer 5

x + y = 32x + 2y = 10

Answer 6

"substitution method"

Answer 7

(x,y) = (-1/3,31/3)

Answer 8

If that is the case, then the system looks like this:
\[x+y=10\]
\[32x+2y=10\]
By substitution, y=(10-x) and 32x+2(10-x)=10.
Solving for x gives x= -1/3.

Answer 9

Now, this is absolutely right...

Answer 10

Both of you are right, but it all comes down to two digits, or no solution....

Answer 11

I see,
From the first equa. x = ....?
Then sub. the result into the second equa.

Answer 12

Or an INFINITE amount

Answer 13

I'm calling shenanigans on this situation.

Answer 14

Tell that to my professor, @CliffSedge

Answer 15

Give me his/her contact information and I will.

Answer 16

Change "no solution" to "none of the above"

Answer 17

Now it's your turn to help me in Philosophy:
Do you think that Nihilism is a complete deconstruction of Platonic Idealism?

Answer 18

@InsanelyChaotic What the purpose of your showing in the OS site???

Answer 19

What do you think....?

Answer 20

The complete destruction of all meaning and all values would lead to an existence of apathy.....

Answer 21

Have you ever attempted to work on any math?

Answer 22

Of course I have. I've attempted all of these. What's your problem?

Answer 23

Tell your professor not give such confusing tasks..Tell him how he is wrong

Answer 24

*not to give

Answer 25

I'll be sure to

Answer 26

@AbhimanyuPudi and I have shown that this system does have a single, unique solution, so that eliminates the possibility of "no solution" or "infinite solutions."
Testing the other two options, {(1,2), (2,3)}:
{1,2}+{2,3}=32{1,2}+2{2,3}
{3=36=10 False, 5=70=10 False}
So none of the answer choices are valid.

Answer 27

Maybe you should email your professor the link to this thread and the other one. Let him/her see our critique.

Answer 28

@CliffSedge well you are doing a great job. you must be very patient i guess

Answer 29

again no option!!

Answer 30

@CliffSedge hahaha..He is gonna piss off

Answer 31

Eh, I think this stuff is fun, so it's worth sticking around to play with it.

Answer 32

" and I have shown that this system does have a single, unique solution" You said it yourself, there is no solution which is provided. @CliffSedge

Answer 33

You are patient, I could never be this patient with math

Answer 34

The answer is (E) "None of the Above."

Answer 35

I agree

Answer 36

If only!

Answer 37

I am not as patient as @CliffSedge is...i'll solve for solution but i don't have patience to get the right equations from the answer choices!!!

Answer 38

Do you both want an example?

Answer 39

Well, take this as a lesson in the importance of having a well-posed problem in mathematics. I think, really, the best thing you can do in this situation is to ignore the answer choices and provide the correct solution.

Answer 40

Ya..whats that example?

Answer 41

I believe that as well, but if that answer is not provided, which makes the student think that their answer is not valid

Answer 42

One sec

Answer 43

re: "I believe that as well, but if that answer is not provided, which makes the student think that their answer is not valid"
And that is impetus to go back and check your work, but if you are confident after reworking it that your solution is correct, then you have to either ignore the choices given or assume that the question was misstated.

Answer 44

I agree once again @CliffSedge

Answer 45

5x + y=9
4x + 3y = 16

x= 1 y=4
(1,4)



Pick either equation and solve for one of the variables. When you used the elimination method to solve systems of equations, you were able to choose the variable you wanted to eliminate. Here, you will choose the equation and the variable for which you’d like to solve.
Since the y variable in the first equation does not have a coefficient, you might find it easiest to isolate. Although you’re welcome to try any of the others! This first equation is five x plus y equals nine. To isolate y, subtract five x from both sides of the equals sign. Now the variable y is written in terms of x.

Substitute the expression for the isolated variable into the other equation. Since you know that y has the same value as negative 5 x plus 9, you can replace y in the second equation with that expression, to obtain a new equation.
Now solve the new equation. Distribute the 3. Combine like terms. Isolate the variable by subtracting the constant from both sides of the equal sign. Simplify. Divide both sides by negative 11. x equals 1. Half way there!

Substitute the value of x into one of the original equations and solve. You may choose either equation, but the second equation is shown here. Substitute one for the variable x. Simplify. Isolate the variable by subtracting the constant from both sides of the equal sign. Simplify. Divide both sides of the equation by three. You found the value for the second variable, y equals 4.

The solution to this system of equations is the point 1 comma 4. Remember, this means when you substitute x equals 1 and y equals 4 into both equations you will get true equations. When this system is graphed, two lines cross at the point 1 comma 4.

Answer 46

I find it very odd that you had two problems in a row with that same flaw.

Answer 47

And that is impetus to go back and check your work, but if you are confident after reworking it that your solution is correct, then you have to either ignore the choices given or assume that the question was misstated.


You are correct, but I've always personally believed in the professor being correct

Answer 48

Quotation marks above*

Answer 49

Never assume the professor is correct. Trust the math, not the person.

Answer 50

Hahaha..believe me, I never trusted what professors say unless i learn or do it. And i strongly belive in whatever i get as answer.

Answer 51

Read the motto at the top of this page: http://themathpage.com/

Answer 52

Both of you are very confident in math

Answer 53

*believe

Answer 54

Thank you for showing that, I understand :)

Answer 55

Mathematics is the only area of human thought where things can be proven to be true with certainty. (There's a little philosophy back atcha)

Answer 56

Where are you guys from?

Answer 57

But back to the example:

5x + y = 9
4x + 3y = 16
subtract -5x on both sides
y= -5x +9

Answer 58

Krypton.

Answer 59

its not a little philosophy...lol

Answer 60

@CliffSedge Touche

Answer 61

That was a touch of phil!

Answer 62

(Epistemology is another hobby of mine. I highly recommend the book, "The Beginning of Infinity" by David Deutch)
But anyway, back to your example...

Answer 63

"5x + y = 9
4x + 3y = 16
subtract -5x on both sides
y= -5x +9"

This is all correct so far, and the next step is to solve
4x+3y=16 for x, then sub in the y from eq.1 to eq.2

Answer 64

I'll definitely check it out, thank you. I've been looking for good books to read. Most of my friends suggest Twilight and the Greys book

Answer 65

y= -5 x +9
4x + 3y = 16

Answer 66

y= -5x +9
4x + 3 (-5x+9) = 16

Answer 67

4x = 16
4x - 15x +27 = 16
-11 x +27 = 16
(subtract "-27" on both sides)

Answer 68

-11x = -11
(divide "-11" on both sides)

Answer 69

x= 1

Answer 70

Right-o...

Answer 71

x= 1
4x +3y = 16
4 (1) + 3y = 16
4 +3y= 16
(subtract -4 on both sides)

Answer 72

Equals: 3y=12

Answer 73

3y/3 = 12/3
y= 4

Answer 74

*solution: (1, 4)

Answer 75

Are there any errors....?

Answer 76

No, that's the usual way to do it.

Answer 77

Nope..

Answer 78

Then why is the other question difficult?

Answer 79

The other questions were very different for an important reason.

Answer 80

To get me to "think"?

Answer 81

If you separate them into two equations, the other question would be as easy as the one you solved now

Answer 82

No, I think they were just wrong.

Answer 83

You both have opposing views

Answer 84

I'm fairly sure i didn't separate them correctly.

Answer 85

the questions were not wrong, the answer choices were wrong

Answer 86

The other questions were of the form
ax + by = cx + dy = e, which is called a compound equality and is generally bad form; it's a like run-on sentence in English grammar.

Answer 87

But it is a part of math; whether it is good or bad

Answer 88

Sure, but we see the trouble it is leading to.

Answer 89

I'm not a fan of run-on sentences

Answer 90

You get the same form of equations when you go higher in your education...while solving 3D-geometry

Answer 91

Trouble is a common thing for learners...Overcoming them is very important!!!

Answer 92

You both should get an A+

Answer 93

Thank you but why? I am a high-school graduate. So, its quite natural that I know better than school students. You will be better than me if you work hard..just as you solved the above problem

Answer 94

I'm still going with the assumption that the system of equations was not stated correctly.

We saw that x+y=32x+2y=10 yielded, via separation,
x+y=10
32x+2y=10
a solution that was not an option.
I find it more likely that the system is actually supposed to be something else.

Let's assume for the moment, that x+y=32x+2y=10 is actually a case of not separating the two equations properly. What if it is actually
x+y=3
2x+2y=10
?

Then you will find that there is no solution.

Shall I test this hypothesis on the other question?

Answer 95

Hypothesis was tested, and I believe it to be correct. The system was not clearly delineated. They are not compound equalities. They were simply typographical errors; probably from not properly copying the text.

Answer 96

NO SOLUTION!!!!! :)