Copyright

when you solve a system of equations by the substitution method, how do you determine whether the...

Question:

when you solve a system of equations by the substitution method, how do you determine whether the system of equations is inconsistent?

Inconsistent equations

Inconsistent set of equations are those that are parallel and do not have a common point of meeting. Such a set of equations cannot be solved as there is no solution possible.

Answer and Explanation:

Suppose you have two sets of parallel equations with unequal constants {eq}c_1 {/eq} and {eq}c_2 {/eq} as follows:

(eq. 1): {eq}ax + by = c_1 {/eq}

(eq. 2): {eq}ax + by = c_2 {/eq}

We can write (eq. 1) as:

{eq}x = \ \frac{c_1 - by}{a} {/eq}

We can replace this value of x in (eq. 2) as:

{eq}a\ \frac{c_1 - by}{a} + by = c_2 {/eq}

=> {eq}c_1 - by + by = c_2 {/eq}

=> {eq}c_1 = c_2 {/eq}

This is not possible since the constants are not equal.

Hence, when solving two equations we reach a point that no variables are left and two unequal numbers are equating to zero, we can claim that the set of equations are inconsistent.


Learn more about this topic:

Loading...
Inconsistent System of Equations: Definition & Example

from High School Algebra II: Homework Help Resource

Chapter 8 / Lesson 9
12K

Related to this Question

Explore our homework questions and answers library