# Solve the systems of equations. 2a-b = -2 a+b = 4

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### 3 Answers

You also may use elimination, hence, you need to add the bottom equation to the top equation, such that:

`2a - b + a + b = -2 + 4 => 3a = 2 => a = 2/3`

Replacing `2/3` for a in any equation, either top, or bottom, yields:

`2/3 + b = 4 => b = 4 - 2/3 => b = (12 - 2)/3 => b = 10/3`

**Hence, evaluating the solution to simultaneous equations, yields `a = 2/3, b = 10/3.` **

The solution of

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

a+b = 4 ...(2)

has to be determined.

(1) + (2)

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

3a = 2

a = 2/3

(1) - 2*(2)

2a - b - 2a - 2b = -2 - 8

-3b = -10

b = 10/3

The solution of the system of equations is 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}.**