document.write( "Question 1197248: Solve by elimination method\r
\n" ); document.write( "\n" ); document.write( "1. x+4y=16
\n" ); document.write( " 3x+5y=20\r
\n" ); document.write( "\n" ); document.write( "2. Bx+4y=16
\n" ); document.write( " 4x-7y=26\r
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Algebra.Com's Answer #830442 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "I'll do problem 1 to get you started.\r
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\n" ); document.write( "\n" ); document.write( "The given system is this
\n" ); document.write( "x+4y = 16
\n" ); document.write( "3x+5y = 20\r
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\n" ); document.write( "\n" ); document.write( "Triple everything in the first equation to go from
\n" ); document.write( "x+4y = 16
\n" ); document.write( "to
\n" ); document.write( "3x+12y = 48\r
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\n" ); document.write( "\n" ); document.write( "This is done so that the x terms have the same coefficient.\r
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\n" ); document.write( "\n" ); document.write( "Here's what the system of equations looks like now
\n" ); document.write( "3x+12y = 48
\n" ); document.write( "3x+5y = 20\r
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\n" ); document.write( "\n" ); document.write( "Now subtract the equations straight down
\n" ); document.write( "3x-3x turns into 0x or 0, so the x terms go away
\n" ); document.write( "12y-5y turns into 7y
\n" ); document.write( "48-20 turns into 28\r
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\n" ); document.write( "\n" ); document.write( "We get 0x+7y = 28 or 7y = 28
\n" ); document.write( "Divide both sides by 7 to get y = 4\r
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\n" ); document.write( "\n" ); document.write( "Now use this y value to find x.
\n" ); document.write( "We can use it with any equation involving x and y mentioned earlier.
\n" ); document.write( "I'll use the first equation
\n" ); document.write( "x+4y = 16
\n" ); document.write( "x+4*4 = 16
\n" ); document.write( "x+16 = 16
\n" ); document.write( "x = 16-16
\n" ); document.write( "x = 0\r
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\n" ); document.write( "\n" ); document.write( "Answer: The solution is (x,y) = (0,4)\r
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\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "Plug x = 0 and y = 4 into the first equation
\n" ); document.write( "x+4y = 16
\n" ); document.write( "0+4*4 = 16
\n" ); document.write( "16 = 16
\n" ); document.write( "That works out. Now do the same for the second equation
\n" ); document.write( "3x+5y = 20
\n" ); document.write( "3*0+5*4 = 20
\n" ); document.write( "20 = 20
\n" ); document.write( "That is confirmed as well.
\n" ); document.write( "Both equations are true for x = 0 and y = 4, which fully confirms the solution.
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