Which of the following is a solution to the equation y = 3x - 1: (a) (2, -3) (b) (1, 2) (c) (0, -1) (d) (1/2, 0)

Solution:

We will substitute x-coordinate and y-coordinate in the equation y = 3x - 1 to check if the given points are the solution of the equation.

(a) Substitute x = 2 and y = -3 in y = 3x - 1

-3 = 3 (2) - 1

-3 = 6 - 1

-3 = 5, which is not possible

So, (2, -3) is not a solution of y = 3x - 1

(b) Substitute x = 1 and y = 2 in y = 3x - 1

2 = 3 (1) - 1

2 = 3 - 1

2 = 2

This is true. So, (1, 2) is a solution of y = 3x - 1

(c) Substitute x = 0 and y = -1 in y = 3x - 1

-1 = 3 (0) - 1

-1 = 0 - 1

-1 = -1

This is true. So, (0, -1) is a solution of y = 3x - 1

(d) Substitute x = 1/2 and y = 0 in y = 3x - 1

0 = 3 (1/2) - 1

0 = 3/2 - 1

0 = 1/2, which is not possible.

So, (1/2, 0) is not a solution of y = 3x - 1

Therefore, the solutions of y = 3x - 1 are (1, 2) and (0, -1)

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Which of the following is a solution to the equation y = 3x - 1

Summary:

The solutions of y = 3x - 1 are (1, 2) and (0, -1)