How do you solve #2x + y = 5# and #y = 3x + 2# using substitution?

2 Answers
Jul 30, 2016

Answer:

#x=3/5#
#y=19/5#

Explanation:

#2x+y=5#
Putting #y=3x+2# in the above equation we get
#2x+3x+2=5#
or
#5x+2=5#
or
#5x=5-2#
or
#5x=3#
or
#x=3/5#=======Ans #1#
By putting #x=3/5# in the equation #y=3x+2#
we get
#y=3(3/5)+2#
or
#y=9/5+2#
or
#y=(9+2(5))/5#
or
#y=(9+10)/5#
or
#y=19/5#=====Ans #2#

Jul 30, 2016

Answer:

#x = 3/5, y = 3 4/5#

Explanation:

This type of question is particularly common when working with straight lines.

Note that there is a single #y# term in both equations.

#y = -2x+5" and " y = 3x +2#

At the point where the two lines intersect, the #x- and y-# values are equal.

If #" y = y" "# it follows that:

#3x +2 =-2x+5#

#5x = 3#

#x = 3/5#

There are now two equations to find a value for y. If we get the same answer for each we will know our answers are correct.

#y = 3xx 3/5 +2 = 3 4/5" "y = -2 xx3/5 +5 = 3 4/5#