document.write( "Question 92527: Solve the system by substitution.
\n" ); document.write( " x + 5y = 0
\n" ); document.write( " –2x – 4y = 6\r
\n" ); document.write( "\n" ); document.write( "A) (–5, -1) B) (5, 1) C) (–5, 1) D) (5, -1)\r
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Algebra.Com's Answer #67357 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: Solving a linear system of equations by subsitution

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\n" ); document.write( " Lets start with the given system of linear equations
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\n" ); document.write( " \"1%2Ax%2B5%2Ay=0\"
\n" ); document.write( " \"-2%2Ax-4%2Ay=6\"
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\n" ); document.write( " Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.
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\n" ); document.write( " Solve for y for the first equation
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\n" ); document.write( " \"5%2Ay=0-1%2Ax\"Subtract \"1%2Ax\" from both sides
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\n" ); document.write( " \"y=%280-1%2Ax%29%2F5\" Divide both sides by 5.
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\n" ); document.write( " Which breaks down and reduces to
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\n" ); document.write( " \"y=0-%281%2F5%29%2Ax\" Now we've fully isolated y
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\n" ); document.write( " Since y equals \"0-%281%2F5%29%2Ax\" we can substitute the expression \"0-%281%2F5%29%2Ax\" into y of the 2nd equation. This will eliminate y so we can solve for x.
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\n" ); document.write( " \"-2%2Ax%2B-4%2Ahighlight%28%280-%281%2F5%29%2Ax%29%29=6\" Replace y with \"0-%281%2F5%29%2Ax\". Since this eliminates y, we can now solve for x.
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\n" ); document.write( " \"-2%2Ax-4%2A%280%29-4%28-1%2F5%29x=6\" Distribute -4 to \"0-%281%2F5%29%2Ax\"
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\n" ); document.write( " \"-2%2Ax%2B0%2B%284%2F5%29%2Ax=6\" Multiply
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\n" ); document.write( " \"-2%2Ax%2B0%2B%284%2F5%29%2Ax=6\" Reduce any fractions
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\n" ); document.write( " \"-2%2Ax%2B%284%2F5%29%2Ax=6%2B0\"Add \"0\" to both sides
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\n" ); document.write( " \"-2%2Ax%2B%284%2F5%29%2Ax=6\" Combine the terms on the right side
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\n" ); document.write( " \"%28-10%2F5%29%2Ax%2B%284%2F5%29x=6\" Make -2 into a fraction with a denominator of 5
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\n" ); document.write( " \"%28-6%2F5%29%2Ax=6\" Now combine the terms on the left side.
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\n" ); document.write( " \"cross%28%285%2F-6%29%28-6%2F5%29%29x=%286%2F1%29%285%2F-6%29\" Multiply both sides by \"5%2F-6\". This will cancel out \"-6%2F5\" and isolate x
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\n" ); document.write( " So when we multiply \"6%2F1\" and \"5%2F-6\" (and simplify) we get
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\n" ); document.write( " \"x=-5\" <---------------------------------One answer
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\n" ); document.write( " Now that we know that \"x=-5\", lets substitute that in for x to solve for y
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\n" ); document.write( " \"-2%28-5%29-4%2Ay=6\" Plug in \"x=-5\" into the 2nd equation
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\n" ); document.write( " \"10-4%2Ay=6\" Multiply
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\n" ); document.write( " \"-4%2Ay=6-10\"Subtract \"10\" from both sides
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\n" ); document.write( " \"-4%2Ay=-4\" Combine the terms on the right side
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\n" ); document.write( " \"cross%28%281%2F-4%29%28-4%29%29%2Ay=%28-4%2F1%29%281%2F-4%29\" Multiply both sides by \"1%2F-4\". This will cancel out -4 on the left side.
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\n" ); document.write( " \"y=-4%2F-4\" Multiply the terms on the right side
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\n" ); document.write( " \"y=1\" Reduce
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\n" ); document.write( " So this is the other answer
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\n" ); document.write( " \"y=1\"<---------------------------------Other answer
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\n" ); document.write( " So our solution is
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\n" ); document.write( " \"x=-5\" and \"y=1\"
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\n" ); document.write( " which can also look like
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\n" ); document.write( " (\"-5\",\"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( " \"1%2Ax%2B5%2Ay=0\"
\n" ); document.write( " \"-2%2Ax-4%2Ay=6\"
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\n" ); document.write( " we get
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\n" ); document.write( " graph of \"1%2Ax%2B5%2Ay=0\" (red) and \"-2%2Ax-4%2Ay=6\" (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.
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\n" ); document.write( " and we can see that the two equations intersect at (\"-5\",\"1\"). This verifies our answer.
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\n" ); document.write( " Check:
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\n" ); document.write( " Plug in (\"-5\",\"1\") into the system of equations
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\n" ); document.write( " Let \"x=-5\" and \"y=1\". Now plug those values into the equation \"1%2Ax%2B5%2Ay=0\"
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\n" ); document.write( " \"1%2A%28-5%29%2B5%2A%281%29=0\" Plug in \"x=-5\" and \"y=1\"
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\n" ); document.write( " \"-5%2B5=0\" Multiply
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\n" ); document.write( " \"0=0\" Add
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\n" ); document.write( " \"0=0\" Reduce. Since this equation is true the solution works.
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\n" ); document.write( " So the solution (\"-5\",\"1\") satisfies \"1%2Ax%2B5%2Ay=0\"
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\n" ); document.write( " Let \"x=-5\" and \"y=1\". Now plug those values into the equation \"-2%2Ax-4%2Ay=6\"
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\n" ); document.write( " \"-2%2A%28-5%29-4%2A%281%29=6\" Plug in \"x=-5\" and \"y=1\"
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\n" ); document.write( " \"10-4=6\" Multiply
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\n" ); document.write( " \"6=6\" Add
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\n" ); document.write( " \"6=6\" Reduce. Since this equation is true the solution works.
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\n" ); document.write( " So the solution (\"-5\",\"1\") satisfies \"-2%2Ax-4%2Ay=6\"
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\n" ); document.write( " Since the solution (\"-5\",\"1\") satisfies the system of equations
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\n" ); document.write( " \"1%2Ax%2B5%2Ay=0\"
\n" ); document.write( " \"-2%2Ax-4%2Ay=6\"
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\n" ); document.write( " this verifies our answer.
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\n" ); document.write( "\n" ); document.write( "So the answer is C)
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