# Write a system of equations that has no solution equation Working it here will show the differences between the two methods and it will also show that either method can be used to get the solution to a system. In the following pages we will look at algebraic methods for finding this solution, if it exists. If it makes at least one of them false, you need to go back and redo the problem. This will be the very first system that we solve when we get into examples. If a variable already has opposite coefficients than go right to adding the two equations together. Well if you think about it both of the equations in the system are lines.

Do not worry about how we got these values.

### How many solutions does this linear equation have

If fractions are going to show up they will only show up in the final step and they will only show up if the solution contains fractions. Thus these equations are said to be inconsistent, and there is no solution. Note as well that we really would need to plug into both equations. As we saw in the opening discussion of this section solutions represent the point where two lines intersect. Step 2: Multiply one or both equations by a number that will create opposite coefficients for either x or y if needed. It is quite possible that a mistake could result in a pair of numbers that would satisfy one of the equations but not the other one. We already know the solution, but this will give us a chance to verify the values that we wrote down for the solution. Using a graphing calculator or a computer , you can graph the equations and actually see where they intersect. In the following pages we will look at algebraic methods for finding this solution, if it exists. If it makes at least one of them false, you need to go back and redo the problem. Step 5: Solve for second variable. A system of equation will have either no solution, exactly one solution or infinitely many solutions.

So, when solving linear systems with two variables we are really asking where the two lines will intersect. If you need a review on solving linear equations, feel free to go to Tutorial Linear Equations in On Variable. In most practical situations, though, the precision of the calculator is sufficient.

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