# SOLUTION: The sum of two numbers is 6 less than twice the first number. Their difference is 10 less than four times the second number. Find each of the numbers. Enter the larger number in th

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 Click here to see ALL problems on Linear Equations And Systems Word Problems Question 339064: The sum of two numbers is 6 less than twice the first number. Their difference is 10 less than four times the second number. Find each of the numbers. Enter the larger number in the answer box below. Answer by ankor@dixie-net.com(15649)   (Show Source): You can put this solution on YOUR website!Let x = the first number Let y = the other number : Write an equation for each statement: : "The sum of two numbers is 6 less than twice the first number." x + y = 2x - 6 x - 2x + y = -6 -x + y = -6 : "Their difference is 10 less than four times the second number." x - y = 4y - 10 x - y - 4y = -10 x - 5y = -10 : Add the two equations -x + y = -6 +x -5y = -10 ----------------adding eliminates x, find y -4y = -16 y = y = +4 : Find x using the 1st equation -x + y = -6 -x + 4 = -6 -x = -6 - 4 -x = -10 x = +10 : : Check solution of x=10, y=4 with the statement: "Their difference is 10 less than four times the second number." 10 - 4 = 4(4) - 10 6 = 16 - 10 : : Enter the larger number in the answer box below. : I'll let you find the box and do that!