# Solving Problems By Elimination

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.

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.

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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.

This method for solving a pair of simultaneous linear equations reduces one equation to one that has only a single variable.

Once this has been done, the solution is the same as that for when one line was vertical or parallel.

So let’s now use the multiplication property of equality first.

## Solving Problems By Elimination Life In College Essay

You can multiply both sides of one of the equations by a number that will result in the coefficient of one of the variables being the opposite of the same variable in the other equation. Notice that the first equation contains the term 4y, and the second equation contains the term y.If you don't have equations where you can eliminate a variable by addition or subtraction you directly you can begin by multiplying one or both of the equations with a constant to obtain an equivalent linear system where you can eliminate one of the variables by addition or subtraction.Use elimination when you are solving a system of equations and you can quickly eliminate one variable by adding or subtracting your equations together.One child ticket costs .50 and one adult ticket costs .00. Adding or subtracting two equations in order to eliminate a common variable is called the elimination (or addition) method.Once one variable is eliminated, it becomes much easier to solve for the other one.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.Example 3: $$\begin 2x - 5y &= 11 \ 3x 2y &= 7 \end$$ Solution: In this example, we will multiply the first row by -3 and the second row by 2; then we will add down as before.$$\begin &2x - 5y = 11 \color\ &\underline \end\ \begin &\underline} \text\ &19y = -19 \end$$ Now we can find: back into first equation: $$\begin 2x - 5\color &= 11 \ 2x - 5\cdot\color &= 11\ 2x 5 &= 11\ \color &\color \color \end$$ The solution is $(x, y) = (3, -1)$.$$\begin &x 3y = -5 \color\ &\underline \end\ \begin &\underline} \text\ &-13x = 26 \end$$ 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 $(x, y) = (1, -2)$.