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Real numbers a and b satisfy a + ab = 250 a - ab = -240

Enter all possible values of a, separated by commas.

 May 24, 2023
 #3
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a + ab = 250

a - ab = -240

 

Method 1: 

 

Add the two equations so that the ab's cancel out to get: 

2a = 10

so a = 5

 

 

Plug into equations to check: 

5 + 5b = 250

1 + b = 50

b = 49 

5 - 5b = -240

1 - b = -48

b = 49

In both cases, b remains the same, therefore 5 works as an answer

 

Method 2: 

 

Graphing (💀💀💀)

 

(i was too lazy to graph by myself)

 

but yes, a = 5

 May 25, 2023

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