what does 3x-y=13 and 5x+3y=2 in linear system algebralically

Question

please help me!

Answer 1

Substitution method :

The equations are

3x  - y = 13   ---------> (1)

5x + 3y = 2     ---------> (2)

Solve for x from (2)

5x = 2 - 3y

x = (2 - 3y)/5   ---------> (3)

Substitute x value in (1).

3[(2 - 3y)/5]  - y = 13

(6 - 9y - 5y)/5 = 13

6 - 9y - 5y = 65

6 - 14y = 65

- 14y = 59

y = - 59/14

⇒ y = - 59/14.

Substitute y value in (3).

x = 2 - 3(- 59/14)/5 = 205/70 = 41/14

⇒ x = 41/14.

Solution of the system is x = 41/14 and y = - 59/14.