document.write( "Question 1130420: Solve the system of equations by using the elimination method. (If the system is dependent, enter a general solution in terms of c. If there is no solution, enter NO SOLUTION.)
\n" ); document.write( "{3x+ 4y= −8
\n" ); document.write( " x− 5y= −9
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Algebra.Com's Answer #747090 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "\"3x%2B+4y=+-8\"
\n" ); document.write( "\"x-5y=+-9\"\r
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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( " \"3%2Ax%2B4%2Ay=-8\"
\n" ); document.write( " \"1%2Ax-5%2Ay=-9\"
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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 3 and 1 to some equal number, we could try to get them to the LCM.
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\n" ); document.write( " Since the LCM of 3 and 1 is 3, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -3 like this:
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\n" ); document.write( " \"1%2A%283%2Ax%2B4%2Ay%29=%28-8%29%2A1\" Multiply the top equation (both sides) by 1
\n" ); document.write( " \"-3%2A%281%2Ax-5%2Ay%29=%28-9%29%2A-3\" Multiply the bottom equation (both sides) by -3
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\n" ); document.write( " So after multiplying we get this:
\n" ); document.write( " \"3%2Ax%2B4%2Ay=-8\"
\n" ); document.write( " \"-3%2Ax%2B15%2Ay=27\"
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\n" ); document.write( " Notice how 3 and -3 add to zero (ie \"3%2B-3=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( " \"%283%2Ax-3%2Ax%29%2B%284%2Ay%2B15%2Ay%29=-8%2B27\"
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\n" ); document.write( " \"%283-3%29%2Ax%2B%284%2B15%29y=-8%2B27\"
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\n" ); document.write( " \"cross%283%2B-3%29%2Ax%2B%284%2B15%29%2Ay=-8%2B27\" 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( " \"19%2Ay=19\"
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\n" ); document.write( " \"y=19%2F19\" Divide both sides by \"19\" to solve for y
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\n" ); document.write( " \"y=1\" Reduce
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\n" ); document.write( " Now plug this answer into the top equation \"3%2Ax%2B4%2Ay=-8\" to solve for x
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\n" ); document.write( " \"3%2Ax%2B4%281%29=-8\" Plug in \"y=1\"
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\n" ); document.write( " \"3%2Ax%2B4=-8\" Multiply
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\n" ); document.write( " \"3%2Ax=-8-4\" Subtract \"4\" from both sides
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\n" ); document.write( " \"3%2Ax=-12\" Combine the terms on the right side
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\n" ); document.write( " \"cross%28%281%2F3%29%283%29%29%2Ax=%28-12%29%281%2F3%29\" Multiply both sides by \"1%2F3\". This will cancel out \"3\" on the left side.
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\n" ); document.write( " \"x=-4\" 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=-4\", \"y=1\"
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\n" ); document.write( " which also looks like
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\n" ); document.write( " (\"-4\", \"1\")
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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( " \"3%2Ax%2B4%2Ay=-8\"
\n" ); document.write( " \"1%2Ax-5%2Ay=-9\"
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\n" ); document.write( " we get
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\n" ); document.write( " graph of \"3%2Ax%2B4%2Ay=-8\" (red) \"1%2Ax-5%2Ay=-9\" (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 (\"-4\",\"1\"). This verifies our answer.

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\n" ); document.write( "\n" ); document.write( "answer:\r
\n" ); document.write( "\n" ); document.write( "(\"x\",\"+y\") =(\"-4\",\"+1\") \n" ); document.write( "
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