document.write( "Question 1197248: Solve by elimination method\r
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document.write( "1. x+4y=16
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document.write( " 3x+5y=20\r
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document.write( "2. Bx+4y=16
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document.write( " 4x-7y=26\r
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Algebra.Com's Answer #830442 by math_tutor2020(3817)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "I'll do problem 1 to get you started.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The given system is this \n" ); document.write( "x+4y = 16 \n" ); document.write( "3x+5y = 20\r \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "This is done so that the x terms have the same coefficient.\r \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Answer: The solution is (x,y) = (0,4)\r \n" ); document.write( " \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. \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " |