How to find a and b is we are given that a = 2b-1 and 3a= b-2

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We have to find a and b given the following equations:

a = 2b - 1 ...(1)

3a = b-2 ...(2)

We can multiply (1) by three and subtract it from (2)

2 - 3*(1)

=> 3a - 3a = b - 2 - 6b + 3

=> 0 =...

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We have to find a and b given the following equations:

a = 2b - 1 ...(1)

3a = b-2 ...(2)

We can multiply (1) by three and subtract it from (2)

2 - 3*(1)

=> 3a - 3a = b - 2 - 6b + 3

=> 0 = -5b +1

=> 5b = 1

=> b = 1/5

a = 2b - 1

=> 2*(1/5) - 1

=> 2/5 - 5/5

=> a = -3/5

Therefore a= -3/ 5 and b = 1/5

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

Given the equations:

a = 2b -1 ...........(1)

3a = b-2 ................(2)

Then, we have a system of two equations and two variables.

We will use the substitution method to find a and b.

We will substitute (1) into (2).

==> 3a = b-2

==> 3( 2b-1) = b-2

==> 6b - 3 = b-2

Now we will combine like terms.

==> 5b = 1

==> b= 1/5

==> a = 2b-1 = 2(1/5) -1 = 2/5 - 5/5 = -3/5

==> a = -3/5

Approved by eNotes Editorial Team