document.write( "Question 128354This question is from textbook
\n" ); document.write( ": 26. 10m-9n=15 27. 3c-7d= -3 28. 6g-8h=50 30. 3x= -31+2y
\n" ); document.write( " 5m-4n=10 2c+6d= -34 4g+6h=22 5x+6y=23
\n" ); document.write( "

Algebra.Com's Answer #93961 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
I'll do the first two to get you started\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Start with the given system of equations:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"system%2810m-9n=15%2C5m-4n=10%29\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\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 solve for n.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So let's isolate n in the first equation\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"10m-9n=15\" Start with the first equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"-9n=15-10m\" Subtract \"10m\" from both sides\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"-9n=-10m%2B15\" Rearrange the equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"n=%28-10m%2B15%29%2F%28-9%29\" Divide both sides by \"-9\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"n=%28%28-10%29%2F%28-9%29%29m%2B%2815%29%2F%28-9%29\" Break up the fraction\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"n=%2810%2F9%29m-5%2F3\" Reduce\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since \"n=%2810%2F9%29m-5%2F3\", we can now replace each \"n\" in the second equation with \"%2810%2F9%29m-5%2F3\" to solve for \"m\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"5m-4highlight%28%28%2810%2F9%29m-5%2F3%29%29=10\" Plug in \"n=%2810%2F9%29m-5%2F3\" into the first equation. In other words, replace each \"n\" with \"%2810%2F9%29m-5%2F3\". Notice we've eliminated the \"n\" variables. So we now have a simple equation with one unknown.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"5m%2B%28-4%29%2810%2F9%29m%2B%28-4%29%28-5%2F3%29=10\" Distribute \"-4\" to \"%2810%2F9%29m-5%2F3\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"5m-%2840%2F9%29m%2B20%2F3=10\" Multiply\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%289%29%285m-%2840%2F9%29m%2B20%2F3%29=%289%29%2810%29\" Multiply both sides by the LCM of 9. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"45m-40m%2B60=90\" Distribute and multiply the LCM to each side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"5m%2B60=90\" Combine like terms on the left side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"5m=90-60\"Subtract 60 from both sides\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"5m=30\" Combine like terms on the right side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"m=%2830%29%2F%285%29\" Divide both sides by 5 to isolate m\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"m=6\" Divide\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------First Answer------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the first part of our answer is: \"m=6\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since we know that \"m=6\" we can plug it into the equation \"n=%2810%2F9%29m-5%2F3\" (remember we previously solved for \"n\" in the first equation).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"n=%2810%2F9%29m-5%2F3\" Start with the equation where \"n\" was previously isolated.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"n=%2810%2F9%29%286%29-5%2F3\" Plug in \"m=6\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"n=60%2F9-5%2F3\" Multiply\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"n=5\" Combine like terms and reduce. (note: if you need help with fractions, check out this solver)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------Second Answer------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the second part of our answer is: \"n=5\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------Summary------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our answers are:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"m=6\" and \"n=5\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "# 27\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Start with the given system of equations:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"system%283c-7d=-3%2C2c%2B6d=-34%29\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\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 solve for d.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So let's isolate d in the first equation\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"3c-7d=-3\" Start with the first equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"-7d=-3-3c\" Subtract \"3c\" from both sides\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"-7d=-3c-3\" Rearrange the equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"d=%28-3c-3%29%2F%28-7%29\" Divide both sides by \"-7\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"d=%28%28-3%29%2F%28-7%29%29c%2B%28-3%29%2F%28-7%29\" Break up the fraction\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"d=%283%2F7%29c%2B3%2F7\" Reduce\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since \"d=%283%2F7%29c%2B3%2F7\", we can now replace each \"d\" in the second equation with \"%283%2F7%29c%2B3%2F7\" to solve for \"c\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2c%2B6highlight%28%28%283%2F7%29c%2B3%2F7%29%29=-34\" Plug in \"d=%283%2F7%29c%2B3%2F7\" into the first equation. In other words, replace each \"d\" with \"%283%2F7%29c%2B3%2F7\". Notice we've eliminated the \"d\" variables. So we now have a simple equation with one unknown.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2c%2B%286%29%283%2F7%29c%2B%286%29%283%2F7%29=-34\" Distribute \"6\" to \"%283%2F7%29c%2B3%2F7\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2c%2B%2818%2F7%29c%2B18%2F7=-34\" Multiply\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%287%29%282c%2B%2818%2F7%29c%2B18%2F7%29=%287%29%28-34%29\" Multiply both sides by the LCM of 7. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"14c%2B18c%2B18=-238\" Distribute and multiply the LCM to each side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"32c%2B18=-238\" Combine like terms on the left side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"32c=-238-18\"Subtract 18 from both sides\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"32c=-256\" Combine like terms on the right side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"c=%28-256%29%2F%2832%29\" Divide both sides by 32 to isolate c\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"c=-8\" Divide\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------First Answer------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the first part of our answer is: \"c=-8\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since we know that \"c=-8\" we can plug it into the equation \"d=%283%2F7%29c%2B3%2F7\" (remember we previously solved for \"d\" in the first equation).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"d=%283%2F7%29c%2B3%2F7\" Start with the equation where \"d\" was previously isolated.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"d=%283%2F7%29%28-8%29%2B3%2F7\" Plug in \"c=-8\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"d=-24%2F7%2B3%2F7\" Multiply\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"d=-3\" Combine like terms and reduce. (note: if you need help with fractions, check out this solver)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------Second Answer------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the second part of our answer is: \"d=-3\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------Summary------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our answers are:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"c=-8\" and \"d=-3\"\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );