How do you solve # y=x+3# and #y=2x# using substitution?

3 Answers
Mar 29, 2018

Answer:

#x=3,y=6#

Explanation:

#y=x+3---(1)#

#y=2x---(2)#

substitute #y# from #(2) rarr(1)#

#:.2x=x+3#

#=>x=3#

#=>y=2xx3=6#

#x=3,y=6#

a quick mental check in #(1)# verifies the solution

Mar 29, 2018

Answer:

#x=3, y=6#

Explanation:

Substitution in a system means that you write a variable in term of the other(s), and then replace every occurrence of that varable in the other equations.

It's easier done than said! Let's take a look at your system:
#y=x+3#
#y=2x#

Both equations give us an explicit representation of #y#. Take the first one, for example: we can see that #y# and #x+3# are the same thing. This means that, in the second equation, we can replace #y# with #x+3#, obtaining

#x+3=2x#

This is an equation involving #x# alone, and we can solve it as usual:

#x+3=2x -> 3 = 2x-x -> 3 = x#

Once we find one variable, we deduce the other using it's explicit representation: we knew that #y=x+3#, and now we know that #x=2#. Thus, #y=3+3=6#.

PS, note that this was a special case, since both equations were an explicit representation for #y#. We could have simply used transitivity to deduce that, if #y=x+3# and #y=2x#, then #x+3=2x#, and continue as above.

Mar 29, 2018

Answer:

By guessing what is the value of #x# and #y#.

Explanation:

We have to find the value of #y#, which in both is the same value, by substituting the letters with guessed numbers.
We have to guess the value of #x#
Let's make the value of #x# 2.
That will become:
#y# = 2 + 3 and #y# = 22.
Simplify; #y# = 5 and #y#= 4
This can't be right because the #y#'s value is different.
Let's go up by one number: 3
That is:
#y# = 3 + 3 and #y# = 2
3
Which is: #y# = 6 and #y#=6.

The answer is 6.
Hope this helps!!