How do you solve the system of equations #4x-y = -14# and #y = 4x+14# by substitution?

1 Answer
Vikki
Jan 16, 2016

Solution: Infinitely many solutions

Explanation:

Given :
#4x - y = -14#
#y= 4x + 14#

First of all substitution aka "replace" one variable with the given equation.

In this case, we replace the second equation for #y# in the first one....like this

#4x -color(blue)((4x+14)) = -14#

#=> 4x color(blue)(-4x-14)= -14#

#=> -14= -14#

This implied the system have infinitely many solutions , and it's consistent. In another word, when graph both equations , both line will overlapped each other at all points.

Further more, we can write this answer as follow

Let's #x#be any real number, therefore #y= 4x+14#

#(x, 4x+14)#

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