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Solve the system, 2a-b = -2  a+b = 4

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yasmin130 | Student, Undergraduate | (Level 1) Honors

Posted December 4, 2010 at 12:37 PM via web

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Solve the system, 2a-b = -2  a+b = 4

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted December 4, 2010 at 12:39 PM (Answer #1)

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2a-b=-2 ...........(1)

 a+b = 4...............(2)

We have two equations and two variables. Then, we will use the elimination and substitution method to solve.

First, let us add (1) and (2).

==> 2a+ a - b + b = -2 + 4

==> 3a = 2

Now let us divide by 3.

==> a = 2/3

Now we will substitute into (2) to solve for b.

==> a+ b = 4

==> 2/3 + b = 4

==> b = 4 - 2/3

==> b =(12-2) /3 = 10/3

==> b = 10/3.

Then the solution for the system is the pair ( 2/3, 10/3).

Or a = 2/3 and b = 10/3.

 

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted December 4, 2010 at 4:51 PM (Answer #2)

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We'll solve the system using substitution method. We'll change the 2nd equation into:

a+b = 4

a = 4 - b (3)

We'll substitute (3) in (1):

2(4 - b) - b = -2

We'll remove the brackets:

8 - 2b - b = -2

We'll combine like terms and we'll subtract 8 both sides:

-3b = -2 - 8

-3b = -10

We'll divide by -3:

b = 10/3

We'll substitute b in (3):

a = 4 - 10/3

a = (12-10)/3

a = 2/3

The solutions of the system is: {2/3 ; 10/3}.

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