document.write( "Question 527770: the sum of 2 numbers is 13. If twice the larger number is increased by 2, the result is equal to 5 times the smaller number. find the numbers. [show all work] \n" ); document.write( "
Algebra.Com's Answer #349015 by swincher4391(1107)\"\" \"About 
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Let x be the larger number and y be the smaller number
\n" ); document.write( "Then:\r
\n" ); document.write( "\n" ); document.write( "x+y = 13
\n" ); document.write( "2x+2 = 5y\r
\n" ); document.write( "\n" ); document.write( "We have a system of equations so we can use either the elimination method or substitution method.\r
\n" ); document.write( "\n" ); document.write( "Since we have a coefficient of 1 on the first equation, let's use the substitution method.\r
\n" ); document.write( "\n" ); document.write( "x+y = 13 ----> y = 13-x
\n" ); document.write( "2x+2 = 5y\r
\n" ); document.write( "\n" ); document.write( "Substitute 13-x where you see y.\r
\n" ); document.write( "\n" ); document.write( "2x + 2 = 5(13-x)
\n" ); document.write( "2x + 2 = 65 - 5x\r
\n" ); document.write( "\n" ); document.write( "7x = 63 \r
\n" ); document.write( "\n" ); document.write( "x = 9\r
\n" ); document.write( "\n" ); document.write( "Substitute x=9 back into either original equation.\r
\n" ); document.write( "\n" ); document.write( "9 + y = 13\r
\n" ); document.write( "\n" ); document.write( "y = 4\r
\n" ); document.write( "\n" ); document.write( "Thus our two numbers are 9 and 4.
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