# Solving Problems By Elimination

If you multiply the second equation by −4, when you add both equations the y variables will add up to 0. Instead of multiplying one equation in order to eliminate a variable when the equations were added, you could have multiplied both equations by different numbers. Adding 4x to both sides of Equation A will not change the value of the equation, but it will not help eliminate either of the variables—you will end up with the rewritten equation 7y = 5 4x.

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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.

The elimination method of solving systems of equations is also called the addition method.

To solve a system of equations by elimination we transform the system such that one variable "cancels out".

$$3y 2x=6$$ $$\underline$$ $$=8y\: \: \: \: \; \; \; \; =16$$ $$\begin \: \: \: y\: \: \: \: \: \; \; \; \; \; =2 \end$$ The value of y can now be substituted into either of the original equations to find the value of x $$3y 2x=6$$ $$3\cdot 2x=6$$ $$6 2x=6$$ $$x=0$$ The solution of the linear system is (0, 2).

## Genre Essay Writing - Solving Problems By Elimination

To avoid errors make sure that all like terms and equal signs are in the same columns before beginning the elimination.Example 1: $$\begin 3x - y &= 5 \ x y &= 3 \end$$ Solution: In this example we will "cancel out" the y term. $$\begin &\underline} \text\ &4x = 8 \end$$ Now we can find: $x = 2$ In order to solve for y, take the value for x and substitute it back into either one of the original equations.$$\begin \color y &= 3 \ \color y &= 3 \ y &= 1 \end$$ The solution is $(x, y) = (2, 1)$.Multiplication can be used to set up matching terms in equations before they are combined.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.The correct answer is to add Equation A and Equation B.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.And since x y = 8, you are adding the same value to each side of the first equation.If you add the equations above, or add the opposite of one of the equations, you will get an equation that still has two variables.When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.Example $$\begin 3y 2x=6\ 5y-2x=10 \end$$ We can eliminate the x-variable by addition of the two equations.

## Comments Solving Problems By Elimination

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