Question

Solve for A and B.
2a=a+b=3b-5

Answer 1

Whenever we see letters in an equation or such, and we are not given any other equality, we just threat the variables as if they were numbers and leave them like that.
In this case, we have two equalities, so by transitive property we can split them into two other:
\[2a=a+b\]
\[2a=3b-5\]
So this is pretty much a system of equations.
But as I said, let's solve the first one for a, and then replace:
\[1)2a=a+b\]
\[2)2a=3b-5\]
\[1)a=b\]
Then:
\[2a=3a-5\]
\[a=-5\]
Try doing it for b now.

Answer 2

Isn't it suppose to be a=5 not -5 since 3a-2a is -1a?

Answer 3

b= 5 if a= 5 because they are equal. Right? I hope I am right.

Answer 4

2a = a+b
2a = 3b - 5

a + b = 3b - 5
a = 2b - 5

2(2b) = 3b - 5
4b = 3b - 5
b = -5

2a = a + (-5)
a = -5

Answer 5

oooh Thank you very much!

Answer 6

you have to rechek once again if the solution is satisfied for a = b = -5
let's check it together :

look at the original equation :
2a=a+b=3b-5

put a = - 5 and b = -5, so the equation can be
2a=a+b=3b-5
2(-5)=-5+(-5)=3(-5)-5
-10 = -10 = -20

the left side with the middle is okay, but the right side is bad :p

But if we say the solution must be is a = b =5, lets check too
2a=a+b=3b-5
2(5)=5+5=3(5)-5
10 = 10 = 10
LHS = the middle = RHS

i think a = b = 5 is right answer

Answer 7

\[2a=a+b=3b-5 \]Looking at just the left portion:
\[2a = a+b\]Subtract \(a\) from both sides\[2a - a = a -a + b\]\[a = b\]We've established a straightforward relationship between \(a\) and \(b\), but we still don't know their values.
Now the right portion:
\[a+b = 3b-5\]But we know that \(a = b\) so we can write that as \[b+b = 3b -5\]subtract \(2b\) from each side\[2b-2b = 3b-2b-5\]\[0=b-5\]\[b=5\]\[a = b = 5\]

Answer 8

Thank you sooo much!!!! :)