# Write a system of equations that has infinite solutions and no solutions

How many points in common does each system of lines reveal? They never intersect, so there is no point that lies on both lines, and no solution to the system. B The system has one solution. The red point is the solution of the system. To find the solution to systems of linear equations, you can any of the methods below:. She draws the following graph, which accurately shows parts of the two lines in the system. The slope is not readily evident in the form we use for writing systems of equations.

There may be many pairs of x and y that make the first equation true, and many pairs of x and y that make the second equation true, but we are looking for an x and y that would work in both equations.

For example, in The second equation is just two times the first equation, so they are actually equivalent and would both be equations of the same line. Graphing a Real-World Context Systems may be written differently when they are applied to real-world situations, but a solution for the system must still be a set of values that is true for all equations.

We will only look at the case of two linear equations in two unknowns. The fact that they both have the same slope may not be obvious from the equations, because they are not written in one of the standard forms for straight lines.

C The system has two solutions. The graphs of equations within a system can tell us how many solutions exist for that system. In the following pages we will look at algebraic methods for finding this solution, if it exists.

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