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Write these two equations so one is directly above the other as follows:
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\n" ); document.write( "x - y = 5
\n" ); document.write( "x + y = 3
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\n" ); document.write( "Notice now that the two y terms (one in the top equation and one in the bottom) are equal
\n" ); document.write( "but opposite in sign. Therefore, if you add the two equations vertically in columns you
\n" ); document.write( "will add -y and +y and they will cancel out.
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\n" ); document.write( "Adding the two equations vertically results in the two +x terms adding to 2x, the two y terms
\n" ); document.write( "canceling each other because they are equal but of opposite signs, and, on the right side,
\n" ); document.write( "the 5 and the 3 add to 8. So what you are left with as the sum is:
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\n" ); document.write( "2x = 8
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\n" ); document.write( "Solve this equation by dividing both sides by 2 because 2 is the multiplier of the x term.
\n" ); document.write( "When you divide both sides by 2 the equation becomes:
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\n" ); document.write( "x = 4
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\n" ); document.write( "Now you know the value of x. You can return to either of the two original equations
\n" ); document.write( "and substitute 4 for x. Then solve for y. Let's return to the equation:
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\n" ); document.write( "x + y = 3
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\n" ); document.write( "Substitute 4 for x and you get:
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\n" ); document.write( "4 + y = 3
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\n" ); document.write( "Get rid of the 4 on the left side by subtracting 4 from both sides and you have:
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\n" ); document.write( "y = 3 - 4 = -1
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\n" ); document.write( "So you have found the common solution for both equations as x = 4 and y = -1. If you graph
\n" ); document.write( "the two equations you will find that their graphs cross at the (x, y) point (4, -1).
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\n" ); document.write( "You can check this answer by going to each of the two original equations, substituting
\n" ); document.write( "4 for x and -1 for y, and seeing if both sides of the equation are still equal.
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\n" ); document.write( "Go to the original top equation:
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\n" ); document.write( "x - y = 5
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\n" ); document.write( "Replace x with 4 and y with -1 and you have:
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\n" ); document.write( "4 - (-1) = 5
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\n" ); document.write( "Which becomes:
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\n" ); document.write( "4 + 1 = 5
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\n" ); document.write( "That's true. So next go to the bottom of the original equations:
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\n" ); document.write( "x + y = 3
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\n" ); document.write( "Replace x with 4 and y with -1 and you have:
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\n" ); document.write( "4 + (-1) = 3
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\n" ); document.write( "Which becomes:
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\n" ); document.write( "4 - 1 = 3
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\n" ); document.write( "And that is true also. Therefore, our answer is correct. When x = 4 and y = -1 both equations
\n" ); document.write( "are true, therefore this is a common solution.
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\n" ); document.write( "Hope this helps you to understand the problem a little better.
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