document.write( "Question 119195: I submitted this question earlier but there was a typo I apologize to whoever read it. Here it is again. I need to find out how to solve the following problem using the addition or subtraction property. I need to find the values of x and y in these equations: 9x-2y=15 and 4x+3y=-5. It is very important that I see the work because I want to know exactly how to do it for future problems. \n" ); document.write( "
Algebra.Com's Answer #87288 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition

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\n" ); document.write( " Lets start with the given system of linear equations
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\n" ); document.write( " \"9%2Ax-2%2Ay=15\"
\n" ); document.write( " \"4%2Ax%2B3%2Ay=-5\"
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\n" ); document.write( " In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).
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\n" ); document.write( " So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.
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\n" ); document.write( " So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 9 and 4 to some equal number, we could try to get them to the LCM.
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\n" ); document.write( " Since the LCM of 9 and 4 is 36, we need to multiply both sides of the top equation by 4 and multiply both sides of the bottom equation by -9 like this:
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\n" ); document.write( " \"4%2A%289%2Ax-2%2Ay%29=%2815%29%2A4\" Multiply the top equation (both sides) by 4
\n" ); document.write( " \"-9%2A%284%2Ax%2B3%2Ay%29=%28-5%29%2A-9\" Multiply the bottom equation (both sides) by -9
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\n" ); document.write( " So after multiplying we get this:
\n" ); document.write( " \"36%2Ax-8%2Ay=60\"
\n" ); document.write( " \"-36%2Ax-27%2Ay=45\"
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\n" ); document.write( " Notice how 36 and -36 add to zero (ie \"36%2B-36=0\")
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\n" ); document.write( " Now add the equations together. In order to add 2 equations, group like terms and combine them
\n" ); document.write( " \"%2836%2Ax-36%2Ax%29-8%2Ay-27%2Ay%29=60%2B45\"
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\n" ); document.write( " \"%2836-36%29%2Ax-8-27%29y=60%2B45\"
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\n" ); document.write( " \"cross%2836%2B-36%29%2Ax%2B%28-8-27%29%2Ay=60%2B45\" Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.
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\n" ); document.write( " So after adding and canceling out the x terms we're left with:
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\n" ); document.write( " \"-35%2Ay=105\"
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\n" ); document.write( " \"y=105%2F-35\" Divide both sides by \"-35\" to solve for y
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\n" ); document.write( " \"y=-3\" Reduce
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\n" ); document.write( " Now plug this answer into the top equation \"9%2Ax-2%2Ay=15\" to solve for x
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\n" ); document.write( " \"9%2Ax-2%28-3%29=15\" Plug in \"y=-3\"
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\n" ); document.write( " \"9%2Ax%2B6=15\" Multiply
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\n" ); document.write( " \"9%2Ax=15-6\" Subtract \"6\" from both sides
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\n" ); document.write( " \"9%2Ax=9\" Combine the terms on the right side
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\n" ); document.write( " \"cross%28%281%2F9%29%289%29%29%2Ax=%289%29%281%2F9%29\" Multiply both sides by \"1%2F9\". This will cancel out \"9\" on the left side.
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\n" ); document.write( " \"x=1\" Multiply the terms on the right side
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\n" ); document.write( " So our answer is
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\n" ); document.write( " \"x=1\", \"y=-3\"
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\n" ); document.write( " which also looks like
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\n" ); document.write( " (\"1\", \"-3\")
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\n" ); document.write( " Notice if we graph the equations (if you need help with graphing, check out this solver)
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\n" ); document.write( " \"9%2Ax-2%2Ay=15\"
\n" ); document.write( " \"4%2Ax%2B3%2Ay=-5\"
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\n" ); document.write( " we get
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\n" ); document.write( " graph of \"9%2Ax-2%2Ay=15\" (red) \"4%2Ax%2B3%2Ay=-5\" (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).
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\n" ); document.write( " and we can see that the two equations intersect at (\"1\",\"-3\"). This verifies our answer.
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