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Given:
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\n" ); document.write( "y = -3x + 4 and
\n" ); document.write( "y = +x - 4
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\n" ); document.write( "One way you can do this problem is to recognize that each of the two equations has y as its
\n" ); document.write( "left side. For the two left sides to be equal, (y = y in both equations) then the two right
\n" ); document.write( "sides must also be equal. If the two right sides are equal, then we can set them equal in
\n" ); document.write( "the form of an equation as follows:
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\n" ); document.write( "-3x + 4 = x - 4
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\n" ); document.write( "[Note that this follows the algebraic rule that if two quantities are equal to the same quantity
\n" ); document.write( "then the two quantities must also be equal. Both the right sides are equal to y so these two
\n" ); document.write( "right sides must also be equal to each other.]
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\n" ); document.write( "Get rid of the +4 on the left side by subtracting 4 from both sides. When you do that subtraction
\n" ); document.write( "the equation becomes:
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\n" ); document.write( "-3x = x - 8
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\n" ); document.write( "Next, get rid of the x on the right side by subtracting x from both sides to change the
\n" ); document.write( "equation to:
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\n" ); document.write( "-3x - x = -8
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\n" ); document.write( "Combine the two terms on the left side and you have:
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\n" ); document.write( "-4x = -8
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\n" ); document.write( "Solve for x by dividing both sides by -4 and the equation becomes:
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\n" ); document.write( "x = -8/-4 = +2
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\n" ); document.write( "Then you can solve for y by returning to either of the 2 original equations and substituting +2
\n" ); document.write( "for x. Let's return to the equation y = x - 4 and calculate the corresponding value of
\n" ); document.write( "y.
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\n" ); document.write( "y = x - 4
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\n" ); document.write( "Substitute +2 for x and the equation becomes:
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\n" ); document.write( "y = 2 - 4 = -2
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\n" ); document.write( "So the common solution becomes x = 2 and y = -2 or (+2, -2) in point form.
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\n" ); document.write( "Let's return to the other original equation and see if y = -2 and x = +2 are a common solution.
\n" ); document.write( "We start with:
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\n" ); document.write( "y = -3x + 4
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\n" ); document.write( "Substitute -2 for y and +2 for x to get:
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\n" ); document.write( "-2 = -3(2) + 4
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\n" ); document.write( "Do the multiplication on the right side by multiplying -3 times 2 to get:
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\n" ); document.write( "-2 = -6 + 4
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\n" ); document.write( "If you combine the two terms on the right side the equation becomes:
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\n" ); document.write( "-2 = -2
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\n" ); document.write( "And since this is true we know that y = -2 and x = +2 is also a solution of the first equation.
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\n" ); document.write( "Therefore, we have found that y = -2 and x = +2 is the solution for both equations.
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\n" ); document.write( "[This means that the (x, y) coordinate point of (+2, -2) is the point where the graphs of the
\n" ); document.write( "two original equations cross each other.]
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\n" ); document.write( "Hope this helps you to understand the problem and provides you with an understanding of
\n" ); document.write( "the process you can follow to solve the set of equations you were originally given.
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