Question

What is the solution to this system of equations?
x + 4y = 1
2x - 3y = -9

a) (2, -8)
b) (-3, 1)
c) no solution
d) infinitely many solutions

Answer 1

Do you know how to solve systems of equations by substitution or elimination?

Answer 2

yes i do, i start by eliminating the y variable then add what i get there to the other equation then solve for x

Answer 3

That would be B :)
U are right!
and yeah you use the same method that ya used in the previous case :)

Answer 4

Okay, so the first equation looks particularly easy to isolate one of the variables, \(x\). Can you solve it for \(x\)? Then plug the expression you get in to the section equation wherever you find \(x\).

Answer 5

you can also take the choices put them back in the question see if they both are true for that point.

Answer 6

@princeharryyy tell me, how does that work with the "infinitely many" or "no solution" choices? If you find a point in the answer choices that works, how do you know it is the only solution?

Answer 7

@whpalmer you don't have to even solve for them if u take a look at the equations and their slopes and the constants. and that saves all the time.

Answer 8

u know which equation leads to which solutions, whether they have infinite solutions or no solutions. @whpalmer4

Answer 9

Don't be shy, explain how you know that from your initial suggestion: "you can also take the choices put them back in the question see if they both are true for that point."

Answer 10

yeah @whpalmer4 you have some conditions for solvability :)
they make everything so much easier
and i think he meant 'hit and trial'
that's the like the first thing most ppl do :)

Answer 11

1. lines are not parallel neither they are congruent. so yes u k which one is the right answer.

Answer 12

@whpalmer4 so they lead to only 1 solution, So yes I think u shouldn't argument with me over that.

Answer 13

When you tell a student asking for help on such an easy problem that they can find the answer by just trying the answers provided, you do not do them any favors. Many of them will conclude that can always find the answer this way, whereas many exam writers will test deeper understanding by putting in answers to trap those who do not understand and merely seize on what appears to be a correct answer.

Answer 14

And in real life, you usually do not have a set of answers to choose from, you need to find the answer yourself.

Now, anyone interested in showing the OP how to actually solve the system of equations?

Answer 15

i know how to solve this and i only asked to check my work because i wanted complete confidence in the answer, thanks everyone for your help. @Vijeya3 has already helped me in explanation

Answer 16

it is best if you know how to solve without the given options. Also saves time.

Answer 17

@triciaal options save time while solving them takes time, further it depend on the coefficients whether you should solve them by options or not.