Solve each system by the substitution method.

Question

Determine whether the equations are independent, dependent, or inconsistent.
2x + y = 9
2x – 5y = 15

Answer 1

Substitution method :

The equations of linear system are 2x + y = 9 and 2x - 5y = 15.

Solve the equation 1: 2x + y = 9 for y, since the y has a coefficient of 1.

2x + y = 9

y = 9 - 2x.

Substitute the value of y = 9 - 2x in the equation 2 : 2x - 5y = 15 and solve for x.

2x - 5(9 - 2x) = 15

2x - 45 + 10x = 15

12x - 45 = 15

12x = 15 + 45 = 60

 x = 60/12 = 5

⇒ x = 5.

Substitute the value of x = 5 in the equation y = 9 - 2x to find the value of y.

y = 9 - 2(5) = 9 - 10 = - 1.

⇒ y = - 1.

The solution of the system is x = 5 and y = - 1.

Therefore the given system is independent.Because, it has exactly one solution.