What is the solution to the system of equations?

{x+y=6x=y+2

(4, 2)

(6, 4)

(3, 3)

(2, 4)

The solution of the system of equations is (4, 2) ⇒ 1st answer

Step-by-step 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)