solve the following system of linear equations by addition: 2x+2y=26, -3x+3y=-21

Question

solve the folllowing system of linear equations by addition.

Answer 1

Elimination method :

The equations are

      ---------------->(1)

---------------->(2)

Divide each side by 2 to  (1) and Divide each side by 3 to (2).

        ---------------->(3)

   ---------------->(4)

___________

.

Substitute the values in (3).

.

The solution of the system is and .

Comments

The solution of the system 2x + 2y = 26 and - 3x + 3y = - 21 is x = 10 and y = 3.

Answer 2

Addition method :

The system of equations are
2x + 2y = 26     → ( 1 )

- 3x + 3y = - 21 → ( 2 )

Divide eq ( 1 ) by 2 and eq ( 2 ) by 3, then add them, to solve for y.

x + y = 13

- x + y = - 7

( + )_____________

2y = 6

⇒ y = 6/2 = 3.

Substitute the value y = 3 in x + y = 13, and solve for x.

x + 3 = 13

x = 13 - 3

⇒ x = 10.

The solution is x = 10 and y = 3.