Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you solve the following equations by substitution: $8 x - 4 y = 16$ $8x - 4y = 16$ and $y = 2 x - 4 ?$ $y = 2x - 4?$ ?

1 Answer

Oct 21, 2015

There are infinitely many solutions to this pair of equations. (See below for demonstration using substitution).

Explanation:

Given:
[1] $XXX 8 x - 4 y = 16$ $color(white)("XXX")8x-4y=16$
[2] $XXX y = 2 x - 4$ $color(white)("XXX")y=2x-4$

Substituting $(2 x - 4)$ $(2x-4)$ from [2] for $y$ $y$ in [1]
[3] $XXX 8 x - 4 (2 x - 4) = 16$ $color(white)("XXX")8x-4(2x-4)=16$

Simjplifying
[4] $XXX 16 = 16$ $color(white)("XXX")16 = 16$

Since this is true for all pairs $(x, y)$ $(x,y)$ there is no unique solution.
(The equations represent the same line).

Related questions

See all questions in Systems Using Substitution

Impact of this question

1690 views around the world

You can reuse this answer
Creative Commons License