Question

Solve the system of equations by substitution. What is the solution for x?

2x + y = 1
4x + 2y = −1

a. x = 0
b. x = 2
c. There is no x value as there is no solution.
d. x can be any value as there is an infinite number of solutions.

Answer 1

okay so basically you have to set on of the equations equal to y and then plug that value you get for y into the other equation

Answer 2

So solve one of them them put the answer in the other equation?

Answer 3

yep

Answer 4

How would you solve the equation?

Answer 5

eq.1 2x+y=1
eq.2 4x+2y=-1
from eq.1 we solve for y so
y=1-2x
now sub y=1-2x in eq.2
so, 4x+2(1-2x)=-1

Answer 6

okay lets pic the second equation
4x + 2y = -1
subtract the 4x
2y = -1 - 4x
divide by 2
y = (-1 - 4x)/2

Answer 7

if you use the first equation the x's cancel out so i didn't use it

Answer 8

so now plug in y = (-1 - 4x)/2 as the y for your fist equation 2x+y = 1

Answer 9

so it would be 2x + (-1-4x)/2=1 ?

Answer 10

yep

Answer 11

and know just solve for x

Answer 12

however im starting to think its d

Answer 13

exactly the x cancels out which is true so there is an option for that...it will still cancel out ussing your way @Jdosio

Answer 14

Thank you for the help it makes more sense how to solve it now.

Answer 15

oh really... thats strange im getting -3/2
is it canceling out for you ?

Answer 16

Yeah it is

Answer 17

So wouldnt it be d if it was canceling out?

Answer 18

anyway depending on how you decide to go about it you get different values for x which leads me to believe that it is d

Answer 19

i would like to think its C"

Answer 20

Why c?

Answer 21

because the x value cancels leaving -1/2=1 ...

Answer 22

But if the values get canceled out then wouldnt that mean there was just more then one solution

Answer 23

it was my understanding that if you could manage to get any x value then you could cancel out c

Answer 24

i place my bets on d :p

Answer 25

http://www.virtualnerd.com/algebra-1/linear-equations-solve/variables-both-sides-equations/identity-and-no-solution-equations/no-solution-equation-example

Answer 26

But the equation wasnt set up like that

Answer 27

http://www.charleston.k12.il.us/cms/Teachers/math/PreAlgebra/paunit5/L5-4.pdf

Answer 28

but let me know if it was D...