Question

Can someone help me? I've been stuck on this problem and a few others for a long time.
Solve the system of equations by substitution. What is the solution for x? (1 point)
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

2x + y = 1
4x + 2y = -2

Substitution means, solve one of the equations for a variable, like y = ..., then put that in the second equation

Answer 2

For example,

THe first equation : 2x + y = 1, solving for y

y = -2x + 1

Answer 3

Well, math is one of my really bad subjects. So I don't even know where to start to try and figure this out.

Answer 4

No Solution - The two equations of lines, are parallel lines, they dont cross
Infinite Solutions - They are the same line overlapping each other

Answer 5

Alright, no problem, we can go through it a step at a time

Answer 6

Okay thank you

Answer 7

2x + y = 1
4x + 2y = -2

Those are the original equations in the problem, When they ask you about solutions to these equations, they want to know, where do they cross each other on the graph , the x-y plane...

Answer 8

That happens at a point in the plane (x,y) x= something and y= something

Answer 9

That is what these types of problems can look like, they want you to find that solution point (x,y) if there is one

Answer 10

Just where 2 lines cross each other, if they do

Answer 11

This is confusing.. but I am trying to follow along.

Answer 12

I am just describing what these types of problems look like on a graph. Each equation is just a line. The solution to them x= something and y= something is where the 2 lines cross each other.

Answer 13

I have four more questions basically just like this one... so I am trying to understand it so I can answer the other ones. So far I am not getting anywhere. But thank you for trying to explain

Answer 14

2x + y = 1
4x + 2y = -2

Here is the mechanical way to solve them, without knowing anything , just the process steps for substitution.....

Answer 15

Except the others ones aren't asking to substitute, they're just asking to solve the following system of equations.

Answer 16

Solve one equation for y =

First equation 2x + y = 1 solve for y

y = -2x + 1

Answer 17

Good so far?

Answer 18

Yes, but with the other equation do I just do Y= 4x + 2 + -2.. 0r? becuase the 2 is next to the Y

Answer 19

Sorry If I am asking dumb questions

Answer 20

Now that you solved the first equation for y,
y = -2x + 1

Substitute that y into the second equation wherever you see a 'y'

4x + 2y = -2

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

Now you have the second equation , with just an X variable and no Y

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

Answer 21

Now that you substituted , and have an equation with only an X variable, you can solve it for X = ....

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

4x -4x + 2 = -2

0x + 2 = -2

2 = -2 FALSE, this system of 2 equations, has ZERO solutions

Answer 22

Okay, when you go through the work like that it starts to make more sense. But still there is a lot for me to look at to try and get where you find the answer. But it is making more sense so thank you

Answer 23

If you solve and find

A false Statement, like 23 = 10 - there are no solutions
A true statement, like 15 = 15 - there are infinite many solutions

A value for x, then you have to find y, and the solution is the pair (x,y)

Answer 24

So would the answer just be x=0? or is there still more work we have to do

Answer 25

Ok, that is why i wanted to show you the graph, Each of the equations describes a LINE on the graph,

If there are no solutions, they are parallel lines, they do not cross each other
If there are Infinite solutions , they are the same line, overlapping each other
IF there is ONE solution, It is the point they cross on the graph

Answer 26

For this one we solved and just got a false statement

2 = -2 False --- that means there are no solutions for x

Answer 27

If you graphed both of the lines, they would be parallel and not cross each other

Answer 28

So there's just no solution at all. Okay..

Answer 29

right

Answer 30

Thank you. I am starting to understand a little better now.. Do you think you could help me with a few more please?

Answer 31

@DanJS

Answer 32

sure, post up another thread, and put my name in it