If a system of linear equations has infinitely many solutions, then the system is called _____. If a system of linear equations has no solution, then the system is called _____.

Question
Forms of linear equations
If a system of linear equations has infinitely many solutions, then the system is called _____. If a system of linear equations has no solution, then the system is called _____.

2021-02-03
Step 1
System of equations having infinite number of solutions is called dependent system.
System of equations having no solution is called inconsistent system.
Hence,
If a system of linear equations has infinitely many solutions, then the system is called dependent system.
If a system of linear equations has no solution, then the system is called inconsistent system.

Relevant Questions

Find values of a and b such that the system of linear equations has (a) no solution, (b) exactly one solution, and (c) infinitely many solutions.
x + 2y = 3
ax + by = −9
Each equation in a system of linear equations has infinitely many ordered-pair solutions.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
Suppose a nonhomogeneous system of nine linear equations in ten unknowns has a solution for all possible constants on the right sides of the equations. Is it possible to find two nonzero solutions of the associated homogeneous system that are not multiples of each other? Discuss.
Whether the statement "If a system of two linear equations in two variables is dependent, then it has infinitely many solutions" is true or false.
Solve the following system of equations. (Write your answers as a comma-separated list. If there are infinitely many solutions, write a parametric solution using t and or s. If there is no solution, write NONE.)
$$\displaystyle{x}_{{1}}+{2}{x}_{{2}}+{6}{x}_{{3}}={6}$$
$$\displaystyle{x}_{{1}}+{x}_{{2}}+{3}{x}_{{3}}={3}$$
$$\displaystyle{\left({x}_{{1}},{x}_{{2}},{x}_{{3}}\right)}=$$?
$$\displaystyle{5}{x}+{y}={8}$$
$$\displaystyle{x}+{2}{y}={5}$$
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. $$\displaystyle{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}&{0}&−{1}&{3}&{9}\backslash{0}&{1}&{2}&−{5}&{8}\backslash{0}&{0}&{0}&{0}&{0}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}$$