Question

Solve the system using the substitution method. If there is no solution, state so. Can someone please help me to understand how to do this?

y=2x+5
x+y=2

Answer 1

where is equation

Answer 2

Sure but I need an example to help work with. Do you have one?

Answer 3

I have one hold on.

Answer 4

y=2x+5,so
x+2x+5=2,now solve

Answer 5

y=2x+5 and x+y=2

Answer 6

OH this is fine
Now to substitute means to replace one thing with an another...So what are we substituting.? Well that would be an amount for a variable. To solve an equation you can really only have one variable.
y=2x +5 right? ...so replace y with 2x +5 in the other equation so you have only one variable.
x + 2x + 5 = 2
3x + 5 = 2
Subtract 5 and you get -3
3x = -3
Now divide by 3 and you get x = -1
Sorry it was so many lines..but i hope this helps

Answer 7

oh ok @Mpost1994 @roshan2004 Now I see what I was doing wrong I was trying to solve for x but didn't know I could also use y to try and solve the problem explains why it was working lol This is so confusing!

Answer 8

How do you know which variable to use?

Answer 9

You can use any variable you like, you will get the same answer, Don't worry !!!, that's the beauty of equation :-)

Answer 10

You can use any variable you like.. but most of the time it will be obvious which one to use...for example I knew to use y this time because it told me exactly what y = in terms of x that is ..what y equals using only numbers and the x variable. Do you get it? :)

Answer 11

Yes but is this a solution? @Mpost1994 @roshan2004 Because on my hw I am suppose to write either solution-independent no solution-parallel or same line infinitely many dependent how do I know which one to put for this system?

Answer 12

Or how can I determine the answer?

Answer 13

Can you give me the choices seperately again?

Answer 14

A. solution-independent
B. no solution-parallel
C. same line infinitely many dependent

Answer 15

A

Answer 16

Don't you need to solve for y roshan?

Answer 17

@roshan2004 Why A? How did you get that? Can you please explain?

Answer 18

If it's a solution wouldn't there be and x and y-intercepts?

Answer 19

Look at this site and maybe this will explain...alright?
http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson
Pm after you read this okay?

Answer 20

Here's an example I have that the professor did on the board:

Solve by substitution :
3x+y=-1
x+2y=8

1. x+2y=8
-2y -2y x=-2y+8
2. 3(-2y+8)+y=-1
-6y+24+y=-1
-5y+24=-1
-24 -24
-5y=-25 / -5 y=5
3. 3x+5=-1
-5 -5
3x=-6 x=-2

Answer 21

So solution is (-2,5) Independent
But idk how he did this?

Answer 22

Oh well that would what we already did .....just solve for both variables using both equations

Answer 23

y= -x+2
y= 2x + 5
Put those into a graph and solve for the solution ..which is where the lines cross

Answer 24

so y=3?

Answer 25

@Mpost1994

Answer 26

Yes :) -(-1) +2 or 2(-1) +5 both come out to 3 ^.^