Question

Substitution.
x = 3 - 2y
2x + 4y = 6

Answer 1

it is given that x=3-2y
for substitution, it is easier for us to make one variable on left hand side and the others on right hand side.
x is assigned as 3-2y in the question.
we can replace x in 2x+4y=6 with 3-2y
like this:
2(3-2y)+4y=6
Do you understand until this step?
If yes, I will continue my work to show you the next step

Answer 2

Yes i am on and understand that step.

Answer 3

x = 3 - 2y
2x + 4y = 6

simplify the second equation to get
x + 2y = 3

then subtract 2y from both sides
x = 3 - 2y

and realize that the second equation is just the same as the first. and it would be pointless to substitute the same equation into itself.

Answer 4

But doing so would yield

3 - 2y = 3 - 2y

Answer 5

2(3-2y)+4y=6
for the bracket, we can multiply every element by the number outside the bracket, like this:
2(3)-2(2y)
=6-4y
put this back to the original equation
6-4y+4y=6
0=0

Answer 6

This question cannot be solved because of not sufficient condition given

Answer 7

The equations given are actually the same.

Answer 8

For solving two unknowns,
we know that we have to get two equations which are not dependent of each other

Answer 9

I always make sure both equations are simplified first before doing any substitutions.

Answer 10

Usually, that helps avoid any unnecessary steps or dead ends

Answer 11

You have to watch out for them, especially with substitutions because sometimes there is no solution or the lines are parallel.