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

Jan 16, 2016

Solution: Infinitely many solutions

#### Explanation:

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

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

$4 x - \textcolor{b l u e}{\left(4 x + 14\right)} = - 14$

$\implies 4 x \textcolor{b l u e}{- 4 x - 14} = - 14$

$\implies - 14 = - 14$

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 $y = 4 x + 14$

$\left(x , 4 x + 14\right)$