# Solving Elimination Problems The equations of a system are dependent if ALL the solutions of one equation are also solutions of the other equation. The equations of a system are independent if they do not share ALL solutions.

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If your variable drops out and you have a FALSE statement, that means your answer is no solution.

If your variable drops out and you have a TRUE statement, that means your answer is infinite solutions, which would be the equation of the line.

If the system in two variables has one solution, it is an ordered pair that is a solution to BOTH equations.

In other words, when you plug in the values of the ordered pair it makes BOTH equations TRUE.

But first, we have to learn how to work with systems in general.

That is why we use generic variables likeat this point.Here, the first block is the coefficients of the equations, one equation per row.The second block is the variables, one per row and listed in the same order as the coefficients.A consistent system is a system that has at least one solution.An inconsistent system is a system that has no solution.If you do get one solution for your final answer, is this system consistent or inconsistent?If you said consistent, give yourself a pat on the back!In other words, it is where the two graphs intersect, what they have in common.So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.In this case you can write down either equation as the solution to indicate they are the same line. To remove fractions: since fractions are another way to write division, and the inverse of divide is to multiply, you remove fractions by multiplying both sides by the LCD of all of your fractions. If one of the equations is already solved for one of the variables, that is a quick and easy way to go.If you need to solve for a variable, then try to pick one that has a 1 as a coefficient.

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Systems of equations with three variables are only slightly more complicated to solve than those with two variables. The two most straightforward methods of solving these types of equations are by elimination and by using 3 × 3 matrices. To use elimination to solve a system of three equations with.…

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Solving Systems of Equations by Elimination is a method to solve a system of two linear equations. Solving Systems of Equations by Elimination follows a specific process in order to simplify the solutions. The first thing you must do when Solving Systems of Equations by Elimination is to multiply either equation so that when you add them vertically, one of the variables will cancel out.…

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