Question

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

2x + y = 1
4x + 2y = −2

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

Answer 1

Ok, so which equation do you want to handle first? :)

Answer 2

Also, welcome to OpenStudy! :D @casey321123 @~

Answer 3

i am not really understanding how to do this problem

Answer 4

ok, let's take the #1 equation :)

which is 2x + y = 1

Answer 5

now let's solve for y in that equation :D

2x + y = 1


Subtract 2x on both sides, what do you get?

Answer 6

y=1-2x

Answer 7

correct, now we plug that equation into the second equation

Answer 8

4x + 2y = −2


so in place of y over there, we plut in 1-2x

so we get:

4x + 2(1-2x) = -2

solve for x :)

Answer 9

x=-2

Answer 10

4x + 2(1-2x) = -2

First use the distributive property

a(b-c) = ab - ac

so

2(1-2x) = ?

Answer 11

not sure how you got x = -2

Answer 12

so let's do it step by step :)

Answer 13

ok

Answer 14

so what is 2(1-2x) = ?

Answer 15

idk what to do

Answer 16

Use the distributive formula

a(b-c) = ab - ac

so

2(1-2x) = ??

What is 2 x 1 = ?

what is 2 x 2 = ?

Answer 17

2 and 4

Answer 18

ok, good

so 2(1-2x) = 2 - 4x

Answer 19

ok

Answer 20

4x + 2 - 4x = -2

What is 4x - 4x = ?

Answer 21

x

Answer 22

nope

4x - 4x = (x)(4-4)

What is 4-4 =?

Answer 23

0

Answer 24

correct so 4x - 4x = (4-4)(x) = 0x = 0

Answer 25

no solution

Answer 26

so tell me, @casey321123 does \(\sf -2 = 2\)?

Answer 27

exactly! It's no solution! :D

Answer 28

when we get no solution, that means, that the two lines are parallel. :)

Great job! :D