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Answers and Explanations'); parent.frames[0].document.write('

The problems you missed are listed below with answers and explanations.  Look over the explanation for each problem so you can understand why you missed it!

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'); resetdisplay(); for(var i = 0; i <5; i++) { ganswer[i] = prompt(question[i],""); if (ganswer[i] == "quit" || ganswer[i] == "QUIT" || ganswer[i] == "Quit") { break; } q++; if (ganswer[i] == answer[i]) { c++; } else { rightans[i] = 0; w++; } resetdisplay(); } for(var i = 0; i < 10; i++) { if (rightans[i] == 0) { expl = expl + explain[i]; } } parent.frames[0].document.write(expl); parent.frames[0].document.write(""); } question[0] = 'How many axes would be needed to solve a system of 3 variables graphically?'; question[1] = 'What is the best method for solving a system of 3 variables?'; question[2] = 'What is another option besides addition to solve systems of equations? This method usually gets very messy when used with large systems.'; question[3] = 'How many equations are needed in a system of 3 variables?'; question[4] = 'How many equations are needed to solve for 4 different variables?'; answer[0] = '3'; answer[1] = 'addition'; answer[2] = 'substitution'; answer[3] = '3'; answer[4] = '4'; explain[0] = '#1

In order to solve systems of equations and variables graphically, you must first graph and then find the intersection point. Each axis represents one variable. If you have a 3rd variable, you must add a third axis to represent it, or you can not graph the equation at all. Moving into a third axis incorporates 3D graphing, which is very complicated to represent on a 2D surface (such as paper)

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Graphing is too complicated to do acurately with 3 variables. And Substitution can create a huge equation that is difficult to solve. Addition can eliminate a variable without creating a mess of an equation.

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Graphing is also a possiblity, but is not recommended, and not very accurate without the aid of 3D graphing calculators (most people don't have one). Therefore the only accurate option left is substitution, although it is also not recommended. It is better than traphing if you cannot use addition.

"; explain[3] = '#4

If given three variables to successfully eliminate all extra possiblities you must have three different equations (different meaning completely, not just another form of one). If you try to use less equations, it will create a false answer most of the time. So you must have the same number of equations (or more) as you do variables

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If given four variables to successfully eliminate all extra possiblities you must have four different equations (different meaning completely, not just another form of one). If you try to use less equations, it will create a false answer most of the time. So you must have the same number of equations (or more) as you do variables

'; rightans[0] = 1; rightans[1] = 1; rightans[2] = 1; rightans[3] = 1; rightans[4] = 1; //-->