Answer:
The solution of the system of equations is (4 , 2) ⇒ 1st answer
Explanation:
* Lets explain how to solve the system of equations
- In the system of equations there are two equations in two variable
x and y
- There are two ways to solve them:
# Substitution method: substitute one variable from one equation
into the other equation, so the equation will have one variable so
we can solve it
# Elimination method: we try to eliminate on variable from both
equation by addition or subtraction to get one equation in one
variable so we can solve it
* Lets solve the problem
∵ The system of equations has:
x + y = 6 ⇒ (1)
x = y + 2 ⇒ (2)
- We will use the substitution method because the second equation
is x in terms of y
- Substitute equation (2) in equation (1)
- That mean replace x by y + 2
∵ (y + 2) + y = 6
- Add the like terms in the left hand side
∴ (y + y) + 2 = 6
∴ 2y + 2 = 6
- Subtract 2 from both sides
∴ 2y = 4
- Divide both sides by 4
∴ y = 2
- Now substitute the value of y in equation (2)
∵ x = y + 2 ⇒ (2)
∴ x = 2 + 2 = 4
∴ x = 4
∴ The solution of the system of equations is (4 , 2)