Solving systems of equations by addition

Question

What is are the steps for solving a system of equations using the addition method? Something like this example from my homework:

4x+13y=16 2x-13y=8

Answer 1

Addition method

4x+3y = 16 -----------> (1)

2x-13y = 8 -------------> (2)

Add (1) and (2) to solve the varibles.

4x+3y = 16

2x-13y = 8

_____________

6x = 24

x = 24/6

x = 4

Substitute the x value in (1)

4*4+3y = 16

16+3y = 16

Subtrat 16 to each side.

16-16+3y = 16-16

3y =0

Divide by 3 to each side.

3y/3 = 0/3

y = 0

Solution of equations is x = 4, y = 0

Comments

The system of equations are

4x + 13y = 16 → ( 1 )

2x - 13y = 8 → ( 2 )

Answer 2

Addition method :

The system of equations are

4x + 13y = 16 → ( 1 )

2x - 13y = 8    → ( 2 )

Write the equations in column form, and then add them, to solve for x.

4x + 13y = 16

2x - 13y = 8

( + )_______________

6x = 24

⇒ x = 24/6 = 4.

Substitute the value x = 4 in eq (1), and solve for y.

4(4) + 13y = 16

13y = 16 - 16 = 0

⇒ y = 0/13 = 0.

The solution is (x, y) = (4, 0).