Question

Which of the following systems of equations has no solution?

a. 9x + 5y = 1; 15y = 18x − 4
b. -7x − 7 = 3y; -14y − 8 = -6x
c. 4x − 3y = 9; 6y = 8x − 18
d. 7y = 5x − 10; 10x − 14y = 8

Answer 1

Just do trial and error. Go through each one. First solve one equation for one variable then plug whatever you get for that into the second equation. I'll use (a) as an example since that one is not the answer.
The first equation is 9x+5y=1 so solve that for a variable, either x or y. Let's do y. Solving for y, 5y=1-9x or y=(1-9x)/5. Now plug that whole thing into the "y" in the second equation, so 15y=18x-4 turns into 15[(1-9x)/5]=18x-4, and solve that for x, which yields x =45/7. Then take that x and plug it back into the first equation and solve for y, so 9x+5y=1 turns into 9(45/7)+5y=1, which yields y=-398/5. So you have an answer for x and y.

Now do that for the rest of them and you will find that one of them does not give you a number for x and y, it will just give you something like x=x at the end, from which you can't get a value.

Answer 2

that doesnt help me, i have a hard time at multiplying and pluggin in problems and distributing. & it doesnt help that i have dyslexia either.

Answer 3

Check for D..

Answer 4

Lol

Answer 5

Oh ok well we can go step by step then, it'll make more sense the more you practice it over and over; I had a friend with dyslexia who studied engineering in college and that involved a lot of math, so you can do it, just practice. What part of my answer were you confused about? For (a), here is the method:
STEP 1) Solve the first equation for y.
\[9x+5y=1\] Remember in math you can add/subtract/multiply whatever you want to one side as long as you do the exact same thing to the other side, since they are equal. So let's subtract 9x from both sides:\[9x-9x+5y=1-9x\]\[5y=1-9x\] To get rid of the 5 on the left, divide by 5, but if we do it on the left side we must divide everything by 5 on the right side as well, so everything is still equal. \[5y/5 = (1-9x)/5\] \[y=(1-9x)/5\]
STEP 2) Plug that equation for y into the second equation you were given in the system, 15y=18x-4. So that means \[15[(1-9x)/5]=18x-4\] To distribute the 15 into the brackets, just multiply it by the numerator, so \[15(1-9x)/5=18x-4\] This can be simplified because the 15 on top and the 5 on the bottom can be reduced. 15/5 =3 and 5/5=1 so that leaves us with \[3(1-9x)=18x-4\] To distribute the 3, multiply it by each term, so 3*1 - 3*9x, which gives \[3-27x=18x-4\] Then to solve for x, add 27x to each side to get rid of the -27x on the left: \[3-27x+27x=18x+27x-4\]\[3=45x-4\] Then add 4 to each side to get rid of the 4 on the right: \[3+4=45x\]\[7=45x\] Then divide each side by 45 to get x by itself on the right:\[7/45=x\]
STEP 3) Now that you know x, plug it back into the first equation of your system, 9x+5y=1, and solve for y, so you will know both x and y. \[9(7/45)+5y=1\] To distribute the 9, multiply it by the numerator, as before. \[9*7/45+5y=1\] \[63/45+5y=1\] Then subtract 63/45 from both sides so \[5y=1-63/45\] To subtract the two terms on the right they need to have a common denominator. Well, 1 is just equal to 45/45, right? Any number divided by itself is equal to 1. So then : \[5y=45/45-63/45=(45-63)/45=-18/45\] END: So you have your answers x and y now. x was found in STEP 2 and y was found in STEP 3.

That is the complete method step by step. Now do that for your other choices (b), (c), and (d) until you find out that doesn't give you a number for x or y. And if you have trouble while doing one of them, just post the part you're having trouble with here.

Answer 6

See,
5x - 7y = 10

Multiply this equation by 2,

10x - 14y = 20 ----------1
10x - 14y = 8 ------------2

Subtract them and then find x and y if you can..

Answer 7

The method waterineyes uses is MUCH easier but not everyone learns that at the same time. If you do that same method for (c):
4x-3y=9 Move the 3y over to the right and the 9 to the left.
4x-9=3y Multiply everything by 2.
8x-18=6y

The second equation of your system is 6y=8x-18, the same thing as above.
Putting them together and subtracting:
8x-18=6y (first equation)
8x-18=6y (second equation)
Well 8x-8x is 0 and 18-(-18)=36 and 6y-6y=0, so you end up with 36=0, which is nonsense.

So it looks like both (c) and (d) are correct answers to this question...?

Answer 8

Wait, no. (d) isn't.

Answer 9

D is having no solution..

Answer 10

Both C and D are having no solution.

Answer 11

Oh yes you're right, I got hung up on the double negative. @Senior012, does all this make sense?

Answer 12

C has many solution

Answer 13

4x-3y=9=g(x)

6y=8x-18=f(x)

f(x)=4x-3y=9 multiply by 2

8x-6y=18

8x=18+6y

8x-18=6y

same line: infinite solutions

Answer 14

@waterineyes

Answer 15

D has no solution...

Answer 16

C has parallel lines so there are infinitely many solutions for C..

Answer 17

Ah, right. My mistake :)

Answer 18

not parallel they're the same line... on top of eachother