document.write( "Question 624402: Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
\n" ); document.write( "-x-3y=.20
\n" ); document.write( "5x+3y=40 \n" ); document.write( "
Algebra.Com's Answer #392781 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "The Problem:\r\n" );
document.write( "Solve this system of equations using the substitution method.\r\n" );
document.write( "-x-3y=.20\r\n" );
document.write( "5x+3y=40\r\n" );
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document.write( "Solution:\r\n" );
document.write( "Rewrite the first equation in \"x=...\" form.\r\n" );
document.write( "-x-3y=0.20\r\n" );
document.write( "-x=3y+0.20\r\n" );
document.write( "x=-3y-0.20\r\n" );
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document.write( "We see that -3y-0.20 and x are equivalent. Make this substitution in the second equation.\r\n" );
document.write( "5x+3y=40\r\n" );
document.write( "5(-3y-0.20)+3y=40\r\n" );
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document.write( "Simplify the equation and solve for y.\r\n" );
document.write( "-15y-1+3y=40\r\n" );
document.write( "-12y-1=40\r\n" );
document.write( "-12y=41\r\n" );
document.write( "y=-41/12\r\n" );
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document.write( "We know that y=-41/12. We'll keep this value as a fraction for now because it is more accurate \r\n" );
document.write( "than the decimal form. Substitute -42/12 for y in the second equation.\r\n" );
document.write( "5x+3y=40\r\n" );
document.write( "5x+3(-41/12)=40\r\n" );
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document.write( "Simplify and solve for x.\r\n" );
document.write( "5x-41/4=40\r\n" );
document.write( "5x=40+41/4\r\n" );
document.write( "5x=201/4\r\n" );
document.write( "x=(201/4)*(1/5)\r\n" );
document.write( "x=201/20\r\n" );
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document.write( "The solution to the system is the ordered pair (201/20,-41/12).\r\n" );
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document.write( "We need to check this solution in the original equations.\r\n" );
document.write( "-x-3y=.20\r\n" );
document.write( "-(201/20)-3(-41/12)=0.20\r\n" );
document.write( "-201/20+123/12=0.20 (I didn't show all the arithmetic to get LCD=60, add, then reduce)\r\n" );
document.write( "1/5=0.20\r\n" );
document.write( "0.20=0.20 \r\n" );
document.write( "Check!\r\n" );
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document.write( "5x+3y=40\r\n" );
document.write( "5(201/20)+3(-41/12)=40\r\n" );
document.write( "1005/20-123/12=40\r\n" );
document.write( "40=40\r\n" );
document.write( "Check! Check!\r\n" );
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document.write( "That's it. The solution is (201/20,-41/12). Just a note. This system would be much easier to solve \r\n" );
document.write( "with the elimination method. When you add together the original equations, the y-terms cancel \r\n" );
document.write( "out. Some times textbooks have you solve these the least efficient way (just to be evil, I guess!)\r\n" );
document.write( "However, when you have the choice, it's good to look for the most efficient method. Mathematicians \r\n" );
document.write( "are all about working smarter, not harder!\r\n" );
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document.write( "Please email your questions/comments about the solution. I want to make sure you understand, \r\n" );
document.write( "and I'd appreciate the feedback.\r\n" );
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document.write( "Ms.Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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