# Solving Problems By Elimination

Another way of solving a linear system is to use the elimination method.In the elimination method you either add or subtract the equations to get an equation in one variable.

Another way of solving a linear system is to use the elimination method.In the elimination method you either add or subtract the equations to get an equation in one variable.

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

If both variables are eliminated and you are left with a true statement, this indicates that there are an infinite number of ordered pairs that satisfy both of the equations. A theater sold 800 tickets for Friday night’s performance. Combining equations is a powerful tool for solving a system of equations.

$$\begin &x 3y = -5 \color\\ &\underline \end\\ \begin &\underline} \text\\ &-13x = 26 \end$$ Now we can find: $y = -2$ Take the value for y and substitute it back into either one of the original equations.

$$\begin x 3y &= -5 \\ x 3\cdot(\color) &= -5\\ x - 6 &= -5\\ x &= 1 \end$$ The solution is $(x, y) = (1, -2)$.

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.

Example 2: $$\begin x 3y &= -5 \ 4x - y &= 6 \end$$ Solution: Look at the x - coefficients.

Multiply the first equation by -4, to set up the x-coefficients to cancel.

You can use this Elimination Calculator to practice solving systems.

So if you have a system: x – 6 = −6 and x y = 8, you can add x y to the left side of the first equation and add 8 to the right side of the equation.

## Comments Solving Problems By Elimination

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