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2x – 4y = 7
\n" ); document.write( "4x + 2y = 9\r
\n" ); document.write( "\n" ); document.write( "Note that you can't solve this pair of equations by just adding them together because
\n" ); document.write( "there isn't a term in the first equation that is equal to a corresponding term in the
\n" ); document.write( "second equation but that has the opposite sign so that when they are added they cancel.\r
\n" ); document.write( "\n" ); document.write( "You must first do something to one of the equations that make a term in each equation
\n" ); document.write( "have the same term but also have opposite signs. For example, in this problem, what would
\n" ); document.write( "happen if you multiplied all the terms of the bottom equation by 2. The pair of equations
\n" ); document.write( "would then be:
\n" ); document.write( "2x – 4y = 7
\n" ); document.write( "8x + 4y = 18
\n" ); document.write( "Now you can see that the term 4y appears in both equations, but it has a minus sign in
\n" ); document.write( "the first equation and a plus sign in the second equation. Now if you add the two
\n" ); document.write( "equations vertically (this satisfies the need to solve it by addition) the 4y terms
\n" ); document.write( "cancel and the equation you end up with is:
\n" ); document.write( "10x = 25
\n" ); document.write( "Dividing both sides by 10 results in:
\n" ); document.write( "x = 2.5
\n" ); document.write( "You can now solve for y by substituting 2.5 for x in either of the two original equations.
\n" ); document.write( "Let's use the first equation.
\n" ); document.write( "2x-4y = 7
\n" ); document.write( "Put 2.5 in place of x to get:
\n" ); document.write( "2(2.5) - 4y = 7
\n" ); document.write( "Multiply out 2(2.5) and the equation becomes:
\n" ); document.write( "5 - 4y = 7
\n" ); document.write( "Subtract 5 from both sides and the equation reduces to:
\n" ); document.write( "-4y = 2
\n" ); document.write( "Finally divide both sides by -4 and you are left with:
\n" ); document.write( "y = -0.5
\n" ); document.write( "That solves the problem ... x = 2.5 and y=-0.5 are the answers.\r
\n" ); document.write( "\n" ); document.write( "Is that the only way to solve this problem by addition? Nope. Way back at the beginning
\n" ); document.write( "we could have multiplied the top equation by -2. This would have made the pair of
\n" ); document.write( "equations:
\n" ); document.write( "-4x +8y = -14
\n" ); document.write( "4x + 2y = 9
\n" ); document.write( "You can now solve this pair by addition because the minus 4x will cancel with the plus 4x.
\n" ); document.write( "Try it. You should get the same answers for x and y as we did above. \n" ); document.write( "