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2 answers:
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We need a system of equations to solve this. "Difference" is to subtract, and we are taking this difference of the 2 squared unknowns to be 20. That equation is 
. Our "first number is x^2, so 3 times that is 3x^2. "Increased by" is adding to that first number. What we are adding is the second number. The second equation is 
. Let's solve the first equation for x^2: 
and sub that value for x^2 into the second equation. 
and 
. Subtract 60 from both sides and combine the y^2 terms to get 
. Divide both sides by 4 to get y^2 = 16 and y = 4. Let's go back now and solve for x. We will use the fact that y^2 = 16 to solve for x^2 and then take the square root of it. 
, x^2 = 4, so x = 2. Your solutions are x = 2 and y = 4. There you go!