document.write( "Question 151611: Which ordered pair is a solution of the system of equations? (x,y)
\n" ); document.write( "y=3x+1 y=5x-3\r
\n" ); document.write( "\n" ); document.write( "A. (2,3) B. (0,1) C. (1,2) D. (2,7)
\n" ); document.write( "

Algebra.Com's Answer #111441 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
In order to find the answer, let's check all of the possible answers (note: an alternative is to solve the system)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's see if (2,3) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"y=3x%2B1\" Start with the first equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%283%29=3%2A%282%29%2B1\" Plug in \"x=2\" and \"y=3\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"3=3%2A%282%29%2B1\" Evaluate and simplify the left side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"3=7\" Evaluate and simplify the right side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the equation is not true, this means that (2,3) is not a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's see if (2,3) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"y=5x-3\" Start with the second equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%283%29=5%2A%282%29-3\" Plug in \"x=2\" and \"y=3\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"3=5%2A%282%29-3\" Evaluate and simplify the left side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"3=7\" Evaluate and simplify the right side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the equation is not true, this means that (2,3) is not a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since at least one of the equations of the system is false, this means that (2,3) is not a solution. Remember, a solution must satisfy all of the equations in the system.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "B)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's see if (0,1) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"y=3x%2B1\" Start with the first equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%281%29=3%2A%280%29%2B1\" Plug in \"x=0\" and \"y=1\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"1=3%2A%280%29%2B1\" Evaluate and simplify the left side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"1=1\" Evaluate and simplify the right side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the equation is true, this means that (0,1) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's see if (0,1) is are a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"y=5x-3\" Start with the second equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%281%29=5%2A%280%29-3\" Plug in \"x=0\" and \"y=1\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"1=5%2A%280%29-3\" Evaluate and simplify the left side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"1=-3\" Evaluate and simplify the right side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the equation is not true, this means that (0,1) is not a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since at least one of the equations of the system is false, this means that (0,1) is not a solution. Remember, a solution must satisfy all of the equations in the system.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "C)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's see if (1,2) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"y=3x%2B1\" Start with the first equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%282%29=3%2A%281%29%2B1\" Plug in \"x=1\" and \"y=2\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2=3%2A%281%29%2B1\" Evaluate and simplify the left side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2=4\" Evaluate and simplify the right side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the equation is not true, this means that (1,2) is not a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's see if (1,2) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"y=5x-3\" Start with the second equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%282%29=5%2A%281%29-3\" Plug in \"x=1\" and \"y=2\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2=5%2A%281%29-3\" Evaluate and simplify the left side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2=2\" Evaluate and simplify the right side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the equation is true, this means that (1,2) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since at least one of the equations of the system is false, this means that (1,2) is not a solution. Remember, a solution must satisfy all of the equations in the system.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "D)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's see if (2,7) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"y=3x%2B1\" Start with the first equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%287%29=3%2A%282%29%2B1\" Plug in \"x=2\" and \"y=7\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"7=3%2A%282%29%2B1\" Evaluate and simplify the left side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"7=7\" Evaluate and simplify the right side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the equation is true, this means that (2,7) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's see if (2,7) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"y=5x-3\" Start with the second equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%287%29=5%2A%282%29-3\" Plug in \"x=2\" and \"y=7\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"7=5%2A%282%29-3\" Evaluate and simplify the left side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"7=7\" Evaluate and simplify the right side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the equation is true, this means that (2,7) is a solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since all of the equations of the system are true, this means that (2,7) is a solution\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( "Answer:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the solution is D) (2,7)
\n" ); document.write( "
\n" );