How do you solve #y = 5x - 10# and #y = 3x + 8# using substitution?

1 Answer
Feb 5, 2017

Answer:

#(x,y)=(9,35)#
(see below for methodology)

Explanation:

Given
[1]#color(white)("XXX")y=5x-10#
[2]#color(white)("XXX")y=3x+8#

Using [1] we can substitute #5x-10# for #y# in [2]
[3]#color(white)("XXX")5x-10=3x+8#

Simplifying:
[4]#color(white)("XXX")2x=18#

[5]#color(white)("XXX")x=9#

We can now use [5] to substitute #9# for #x# in [1]
[6]#color(white)("XXX")y=5 * (9)-10#

Simplifying
[7]#color(white)("XXX")y=35#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We could (and should) verify this result by substituting
#x=9# and #y=35# in [2]
#color(white)("XXX")35 = 3 * (9) + 8# (correct)