# Define Absolute system of Linear Equations?

Question
Forms of linear equations
Define Absolute system of Linear Equations?

2021-02-22
Step 1
We need to define absolute system of linear equations.
Step 2
Absolute system of Linear equations is a system of linear equations where the equations contain at least one absolute value expression.
For example,
|2x-3|+|5-y|=2
|x+8|+|10-|y||=1

### Relevant Questions

Describe how absolute value equations and inequalities are like linear equations and inequalities and how they differ.
Cramer’s Rule to solve (if possible) the system of linear equations.
$$\displaystyle-{8}{x}_{{1}}+{7}{x}_{{2}}{\mid}-{10}{x}_{{3}}=-{151}$$
$$\displaystyle{12}{x}_{{1}}+{3}{x}_{{2}}-{5}{x}_{{3}}={86}$$
$$\displaystyle{15}{x}_{{1}}-{9}{x}_{{2}}+{2}{x}_{{3}}={187}$$
Cramer’s Rule to solve (if possible) the system of linear equations.
$$\displaystyle{\frac{{{5}}}{{{6}}}}{x}_{{1}}-{x}_{{2}}=-{20}$$
$$\displaystyle{\frac{{{3}}}{{{4}}}}{x}_{{1}}-{\frac{{{7}}}{{{2}}}}{x}_{{2}}=-{51}$$
$$\displaystyle{x}-{y}=-{2}{\left({1},{3}\right)}$$
$$\displaystyle{3}{x}-{y}=-{2}$$
is the ordered pair a solution of the system of linear equations.
or not a solution
Determine if (1,3) is a solution to the given system of linear equations.
$$\displaystyle{5}{x}+{y}={8}$$
$$\displaystyle{x}+{2}{y}={5}$$
Consider a system of three linear equations in three variables. Give examples of two reduced forms that are not row-equivalent if the system is: a) onsistent and dependent. b) Inconsistent
The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. Write the solution in vector form. $$\displaystyle{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}&{0}&−{1}&{3}&{9}\backslash{0}&{1}&{2}&−{5}&{8}\backslash{0}&{0}&{0}&{0}&{0}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}$$