y = 5x - 1 and -15x - 3y = 3, how many solutions does this linear system have?

Solution:

Given:

Equations are y = 5x - 1 and -15x - 3y = 3

5x - y = 1 --- (1)

Also, -15x - 3y = 3 --- (2)

Solving (1) and (2)

Multiplying (1) by 3, we get,

⇒ 15x - 3y = 3 ------(3)

Adding (2) and (3) we get,

⇒ -6y = 6

⇒ y = -1

Put the value of y in (1)

⇒ 5x - (-1) = 1

⇒ 5x = 0

⇒ x = 0

Therefore, the solution of the linear equations is (0, -1) i.e., one solution.

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y = 5x - 1 and -15x - 3y = 3, how many solutions does this linear system have?

Summary:

If y = 5x - 1 and -15x - 3y = 3, the solution of the linear equations is (0, -1) i.e., one solution.