# Write a system of equations that has infinitely many solutions

The no solution case will be identical, but the infinite solution case will have a little work to do. Find all solutions to the system First, note that there are four unknwons, but only thre equations.

When these two lines are parallel, then the system has infinitely many solutions. Example 2 Solve the following system of equations using augmented matrices.

The final column is the constant that will be on the right side of the equation. Bonus In parts acand dthere are infinitely many equations that can be found. I'll do it a little bit different. Keep in mind that finding the solution to a system of linear equations finding the point of intersection of a family of lines are two ways of approaching the same problem.

GO Consistent and Inconsistent Systems of Equations All the systems of equations that we have seen in this section so far have had unique solutions. So this system has infinitely many solutions, as the equations both correspond to the same line and lines have infinitely many points. A matrix is in reduced echelon form when, in addition to being in echelon form, each column that contians a nonzero entry usually made to be 1 has zeros not just below that entry but also above that entry. And of course, we still have our minus 8.

But if you could actually solve for a specific x, then you have one solution. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.

Eigenvalue and Eigenvector Defined Gaussian Elimination The purpose of this article is to describe how the solutions to a linear system are actually found. Now let's add 7x to both sides. We will then need to do a little more work to get the solution and the number of equations will determine how much work we need to do.

Well, what if you did something like you divide both sides by negative 7. In this system it is -2 and in the previous example it was So if you get something very strange like this, this means there's no solution.

All the systems of equations that we have seen in this section so far have had unique solutions. These are referred to as Consistent Systems of Equations, meaning that for a given system, there exists one solution set for the different variables in the system or infinitely many sets of solution.

A system of equations has infinitely many solutions if there are infinitely many values of x and y that make both equations true. A system of equations has no solution if there is no pair of an x-value and a y-value that make both equations true.

This agrees with Theorem B above, which states that a linear system with fewer equations than unknowns, if consistent, has infinitely many solutions.

The condition “fewer equations than unknowns” means that the number of rows in the coefficient matrix is less than the number of unknowns. A system of linear equations can have no solution, a unique solution or infinitely many solutions. A system has no solution if the equations are inconsistent, they are contradictory.

for example 2x+3y=10, 2x+3y=12 has no solution. Systems of Linear Equations: No solutions and infinitely many solutions Example 1: A system with no solutions Consider the system of equations $\begin{cases} \begin{array}{ccccc} 3x & - & 2y & = & 3 \\ 6x & + & k\cdot y & = & 4 \\ \end{array} \end{cases}$ Find. See how some equations have one solution, others have no solutions, and still others have infinite solutions.

Creating an equation with infinitely many solutions. Practice: Number of solutions to equations challenge. Next tutorial. Linear equations word problems.

Write a system of equations that has infinitely many solutions
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