The sum of two numbers is 145. Their difference is 45. What are the numbers?
N + N + 45 = 145 2N = 100 N = 50 N + 45 = 95
Let x and y be the two numbers where x is the larger number. x+y = 145 x-y = 45 x+y = 145 y = 145-x ------------ x-y = 45 x-(145-x) = 45 x-145+x = 45 2x-145 = 45 2x = 45+145 2x = 190 x = 190/2 x = 95 ----------- y = 145-x y = 145-95 y = 50 So the solutions are x = 95 and y = 50 So the two numbers are 95 and 50
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Solve the system of equations using the elimination method. 2x + 4y = 10 4x - y = 11
x + y = 145......(1) x - y= 45.....(2) x= 145 - y from (1) x = 45 + y from (2) 145 - y = 45 + y 2y = 100 y= 50 x - 50 = 45 x = 95
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