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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 16, 2023
 #1
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+1

 

Real numbers a and b satisfy  

a + ab = 250  

a - ab = -240  

Enter all possible values of a, separated by commas.  

 

 

If you add the two equations together                a + ab  =   250  

                                                                           a – ab  = –240  

                                                                          ———————  

you get                                                              2a         =  10  

 

from which                                                                  a  =  5  

 

The problem doesn't ask for b,  

but ... find b by substituting  

a back into a + ab = 250                                    5 + 5b  =  250  

                                                                                5b  =  245  

                                                                                  b  =  49  

 

check b by substituting  

a back into a – ab = –240                                  5 – 5b  =  –240  

                                                                              –5b  =  –245  

                                                                                  b  =  49  

.

 May 16, 2023
 #2
avatar+62 
+1

we can use substitution such that for the first equation, we can rearrange it to solve for

b: a + ab = 250

ab = 250 - a

b = (250 - a) / a

Substituting this expression for "b" into the second equation, we get:

a - ab = -240

a - a(250 - a)/a = -240

a - (250 - a) = -240

2a - 250 = -240

2a = 10

a = 5

if you need to find b, substitute a into one of the equations and simplify the equation.

 May 16, 2023

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