Name: Sandy
Level: grade 11
Who is asking the question: teacher

Qustion:
The sum of the squares of two numbers is 53. Twice the greater, minus the lesser is 11. Find the numbers.
 
Hi Sandy
 
Suppose that the numbers are x and y with x>y. Your two conditions then are

and
2x - y = 11.
 
Solve the second condition for y to get y = 2x - 11 and then substitute into the first giving

which, when simplified, is
. Solving, using the general quadratic, gives x=2 or x=6.8. Since y = 2x - 11 the two numbers are 2 and -7 or 6.8 and 2.6.
 
Cheers,
Penny.