4a = 6 - b
4a = 5 - b

A. There is one solution. The solution is ____.
B. There are infinitely many solutions.
C. There are no solutions.

Question

4a = 6 - b
4a = 5 - b

A. There is one solution. The solution is ____. 
B. There are infinitely many solutions. 
C. There are no solutions.

zzr0ck3r · Answer

multiply the second one by -1 we have
4a = 6-b
-4a = -5+b
add them
0 = 1
thus no solutions

hartnn · Answer

as 4a cannot be simultaneously equal to 6-b and 5-b
this system has no solution.

zzr0ck3r · Answer

that to lol

anonymous · Answer

I would use substitution to solve this system.  Solve for a in the first equation, substitute into the 2nd equation, solve for b.  Then check answers.

zzr0ck3r · Answer

elimination is much faster here

zzr0ck3r · Answer

but hartn gave the best answer imo

anonymous · Answer

It said to solve it using substitution... I guessed it was no solution but I wasnt sure.

hartnn · Answer

now u are.

lgbasallote · Answer

as the old people say, "You can't guess and be sure at the same time"

anonymous · Answer

thank you all!

lgbasallote · Answer

hah i got thanked for being a smartmouth

zzr0ck3r · Answer

by substitutaion
4a = 6 - b
4a = 5 - b

so a = (5-b)/4 plug this into the first equation

4a = 6-b
4(5-b)/4 = 6-b
5-b = 6-b
5=6 thus no solutions

zzr0ck3r · Answer

lol @lgbasallote

lgbasallote · Answer

you could have just substituted 4a to 4a...

zzr0ck3r · Answer

its late

anonymous · Answer

yes, I know but i needed to get this done!

parthkohli · Answer

You could also equate both RHSs. For example,$$y = 3x \ y = 3 + x \ \ \implies 3 + x = 3x$$