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# system

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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
+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
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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