![]() The total number of tickets sold is \(\ 800\). How many of each type of ticket were sold? One child ticket costs $4.50 and one adult ticket costs $6.00. The correct answer is to add Equation A and Equation B.Ī theater sold 800 tickets for Friday night’s performance. Felix may notice that now both equations have a term of \(\ -4 x\), but adding them would not eliminate them, it would give him a \(\ -8 x\). Multiplying Equation B by -1 yields \(\ -3 y-4 x=-25\), which does not help Felix eliminate any of the variables in the system. The correct answer is to add Equation A and Equation B. ![]() Instead, it would create another equation where both variables are present. Felix may notice that now both equations have a constant of 25, but subtracting one from another is not an efficient way of solving this problem. Multiplying Equation A by 5 yields \(\ 35 y-20 x=25\), which does not help Felix eliminate any of the variables in the system. Adding \(\ 4 x\) to both sides of Equation A will not change the value of the equation, nor will it help eliminate either of the variables-Felix will end up with the rewritten equation \(\ 7 y=5+4 x\). Felix will then easily be able to solve for \(\ y\). If Felix adds the two equations, the terms \(\ 4x\) and \(\ -4 x\) will cancel out, leaving \(\ 10 y=30\). Add \(\ 4x\) to both sides of Equation A.If he wants to use the elimination method to eliminate one of the variables, which is the most efficient way for him to do so? Be sure to multiply all of the terms of the equation.įelix needs to find \(\ x\) and \(\ y\) in the following system. These equations were multiplied by 5 and -3 respectively, because that gave you terms that would add up to 0. You arrive at the same solution as before. Substitute \(\ y=10\) into one of the original equations to find \(\ x\). Next add the equations, and solve for \(\ y\). ![]() In order to use the elimination method, you have to create variables that have the same coefficient-then you can eliminate them. The equations do not have any \(\ x\) and \(\ y\) terms with the same coefficient. Multiply Equation A by 5 and Equation B by -3. Let’s remove the variable \(\ x\) this time. ![]() 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. There are other ways to solve this system. Substitute \(\ x=4\) into one of the original equations to find \(\ y\). Rewrite the system, and add the equations. Multiply the second equation by -4 so they have the same coefficient. The equations do not have any \(\ x\) or \(\ y\) terms with the same coefficients. ![]()
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