the sum of two numbers is 63. the larger number minus the smaller number is 9. find the numbers

Question

Solve.Use the elimination method when solving the translated system.

Answer 1

If the numbers are a and b, then a+b=63 and a-b=9. From the first equation a=63-b, so we can substitute this value in the other: 63-b-b=9, 63-2b=9, so 2b=63-9=54 and b=27. From this value of b we can find a: a=27+9=36.

Another way to eliminate a or b is to add the two equations: 2a=72, so a=36; and subtract the second from the first: 2b=54, so b=27.

Answer 2

Given x + y = 63.....(1)
& x - y = 9 .......(2)

Add (This eliminates 'y' (+ y - y = 0) )
2x = 72
x = 36
Subsitute 'x = 36' back into either equ'n to find 'y'.
 

Hence
36 + y = 63
y = 63 - 36
y = 27

Hence two numbers are 27 and 36

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