# Using Linear Systems To Solve Problems

The first trick in problems like this is to figure out what we want to know.This will help us decide what variables (unknowns) to use.

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Now, you can always do “guess and check” to see what would work, but you might as well use algebra!

It’s much better to learn the algebra way, because even though this problem is fairly simple to solve, the algebra way will let you solve any algebra problem – even the really complicated ones.

Just as with the substitution method, the elimination method will sometimes eliminate both variables, and you end up with either a true statement or a false statement.

Recall that a false statement means that there is no solution.

Instead, it would create another equation where both variables are present.

The correct answer is to add Equation A and Equation B.

When using the multiplication method, it is important to multiply all the terms on both sides of the equation—not just the one term you are trying to eliminate.

Note that we solve Algebra Word Problems without Systems here, and we solve systems using matrices in the Matrices and Solving Systems with Matrices section here.

“Systems of equations” just means that we are dealing with more than one equation and variable.

So far, we’ve basically just played around with the equation for a line, which is \(y=mx b\).