document.write( "Question 1205723: Solve the system using the substitution method. If there is exactly one solution, write as an ordered pair. If not, choose one of the other options.\r
\n" ); document.write( "\n" ); document.write( "{(6x,+,2y,=,34),(x,,,=,-4y+24):}\r
\n" ); document.write( "\n" ); document.write( "A. One solution:
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\n" ); document.write( "C. Infinite number of solutions \n" ); document.write( "

Algebra.Com's Answer #842715 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Solve the system using the substitution method. If there is exactly one
\n" ); document.write( "solution, write as an ordered pair. If not, choose one of the other options.
\n" ); document.write( "6x + 2y = 34
\n" ); document.write( "x = -4y + 24
\n" ); document.write( "A. One solution:
\n" ); document.write( "B. No solution
\n" ); document.write( "C. Infinite number of solutions
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document.write( "You are lucky: you are given the system of equations, which is just ready for using the substitution method.\r\n" );
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document.write( "Indeed, the second equation expresses x implicitly via y.\r\n" );
document.write( "So, substitute this expression of second equation into first equation.\r\n" );
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document.write( "You will get then\r\n" );
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document.write( "    6*(-4y+24) + 2y = 34.\r\n" );
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document.write( "Thus, you have now one equation with only one unknown y.\r\n" );
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document.write( "Simplify it and solve for y\r\n" );
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document.write( "    -24y + 144 + 2y = 34\r\n" );
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document.write( "    -24y + 2y = 34 - 144\r\n" );
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document.write( "        -22y  =    -110\r\n" );
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document.write( "           y  =     = 5.\r\n" );
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document.write( "Thus you just found out one unknown y:  y = 5.\r\n" );
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document.write( "To find x, use the second given equation\r\n" );
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document.write( "    x = -4y + 24 = -4*5 + 24 = -20 + 24 = 4.\r\n" );
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document.write( "ANSWER.  The problem has one and only one solution  x= 4,  y= 5.\r\n" );
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document.write( "To check your solution, substitute these found values into equations\r\n" );
document.write( "and make sure that in each equation the number in the left side is the same as in the right side.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with all necessary explanations.\r
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\n" ); document.write( "\n" ); document.write( "From my post, learn how to write your problem, when you post it to this forum.\r
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\n" ); document.write( "\n" ); document.write( "Do not use so many commas: they are unnecessary, so take them out.\r
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\n" ); document.write( "\n" ); document.write( "Simply write each equation in separate line and do not use commas.
\n" ); document.write( "Also, do not use curved brackets: they also are unnecessary.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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\n" ); document.write( "\n" ); document.write( "Come again to this forum soon to learn something new.\r
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