Answered: creating equations with no solutions or…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter9: Systems Of Linear Equations

Section9.3: Solving Problems With Two Variables

Problem 11P

See similar textbooks

Related questions

Question

100%

creating equations with no solutions or infinitely many solutions 8x+42=4(3x+9)+ missing number x

Expert Solution

Step 1

Consider the given equation.

Let the missing number is y.

$\begin{array}{rcl} 8 x + 42 & = & 4 (3 x + 9) + x y \\ 8 x + 42 & = & 12 x + 36 + x y \\ 42 - 36 & = & 12 x - 8 x + x y \\ 6 & = & 4 x + x y \end{array}$

Step 2

Let the value of y is -4.

$6 = 4 x - 4 x 6 \neq 0$

Thus, the equation for no solution is $8 x + 42 = 4 (3 x + 9) - 4 x$ .

Again further simplify the solution.

$\begin{array}{rcl} 8 x + 42 & = & 4 (3 x + 9) + x y \\ 8 x + 42 & = & 12 x + 36 + x y \end{array}$

Let the value of $(- 4 + \frac{6}{x})$

$\begin{array}{rcl} 8 x + 42 & = & 4 (3 x + 9) + x y \\ 8 x + 42 & = & 12 x + 36 + x (- 4 + \frac{6}{x}) \\ 8 x + 42 & = & 12 x + 36 - 4 x + 6 \\ 8 x + 42 & = & 8 x + 42 \\ 0 & = & 0 \end{array}$

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

Knowledge Booster

$Systems of Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell