How do you solve #3x + y = 2# and #4x + y = 20# using substitution?

1 Answer
Mar 14, 2018

Answer:

#(x,y)=(18,-52)#

Explanation:

Given
[1]#color(white)("XXX")3x+y=2#
[2]#color(white)("XXX")4x+y=20#

We can re-arrange [1] into the form:
[3]#color(white)("XXX")y=2-3x#

Then we can substitute (as requested) #(2-3x)# for #y# in [2]
[4]#color(white)("XXX")4x+(2-3x)=20#

Simplifying [4]
[5]#color(white)("XXX")x+2=20#

The subtracting #2# from both sides of [5]
[6]#color(white)("XXX")x=18#

Based on [6], we can now substitute #18# for #x# in [1]
[7]#color(white)("XXX")3 * 18 +y=2#

With some simplification
[8]#color(white)("XXX")54+y=2#

[9]#color(white)("XXX")y=-52#