# Write a system of equations with no solution worksheet

Now lets look at this problem graphically. No solutions? This time, lets begin with the geometry.

## Unique solution of a system of linear equations

A system of linear equations is just more than 1 line, see the picture: Ok, so what is the solution of a system of equations? 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. Use the slider to change the value of k. But not only do they have the same slope, they are actually the same line, and so the two lines intersect in infinitely many points. Answer A system of equation just means 'more than 1 equation. These two equations are really the same line. As you can see, parallel lines are not going to ever meet.

Solution: We treat the "infinitely many solutions" case in much the same way as the "no solutions" case. How to make the lines parallel? Solution: Lets try to do Gauss-Jordan elimination. The two lines become parallel. Answer There can be zero solutions, 1 solution or infinite solutions--each case is explained in detail below.

## System of equations with no solution example

But not only do they have the same slope, they are actually the same line, and so the two lines intersect in infinitely many points. Solution: Lets try to do Gauss-Jordan elimination. Answer There can be zero solutions, 1 solution or infinite solutions--each case is explained in detail below. As you can see, parallel lines are not going to ever meet. Solution: We treat the "infinitely many solutions" case in much the same way as the "no solutions" case. Note: Although systems of linear equations can have 3 or more equations,we are going to refer to the most common case--a stem with exactly 2 lines. How to make the lines parallel?

As you can see, parallel lines are not going to ever meet.

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