Solve the system, 2a-b = -2 a+b = 4

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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.**

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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