1
dependent
None, one or infinitely many.
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
As there is no system of equations shown, there are zero solutions.
NO! A linear system can only have one solution (the lines intersect at one point), no solution (the lines are parallel), and infinitely many solutions (the lines are equivalent).
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
Yes.
Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.
Infinitely many.
Linear algebra is used to analyze systems of linear equations. Oftentimes, these systems of linear equations are very large, making up many, many equations and are many dimensions large. While students should never have to expect with anything larger than 5 dimensions (R5 space), in real life, you might be dealing with problems which have 20 dimensions to them (such as in economics, where there are many variables). Linear algebra answers many questions. Some of these questions are: How many free variables do I have in a system of equations? What are the solutions to a system of equations? If there are an infinite number of solutions, how many dimensions do the solutions span? What is the kernel space or null space of a system of equations (under what conditions can a non-trivial solution to the system be zero?) Linear algebra is also immensely valuable when continuing into more advanced math topics, as you reuse many of the basic principals, such as subspaces, basis, eigenvalues and not to mention a greatly increased ability to understand a system of equations.
A linear equation in n variables, x1, x2, ..., xn is an equation of the forma1x1 + a2x2 + ... + anxn = y where the ai are constants.A system of linear equations is a set of m linear equations in n unknown variables. There need not be any relationship between m and n. The system may have none, one or many solutions.
None, one or infinitely many