Question

Check whether each ordered pair is a solution of the inequality. $$3 x-2 y<2 ;(1,3),(2,0)$$

Short answer

The ordered pair (1,3) is a solution of the given inequality but the ordered pair (2,0) is not a solution.

Step-by-step solution

Substitute the Pair (1,3)

First, we will substitute the values of (x, y) from the first ordered pair into the inequality. Thus, putting x=1 and y=3 into our inequality \(3x - 2y < 2\), we get \(3*1 - 2*3 < 2\).

Evaluate the Inequality for (1, 3)

Now, evaluating the inequality, it becomes -3 < 2, which is true. Thus, (1,3) is a solution for the given inequality.

Substitute the Pair (2,0)

Next, we will substitute the values of (x, y) from the second ordered pair into the inequality. Thus, putting x=2 and y=0 into our inequality \(3x - 2y < 2\), we get \(3*2 - 2*0 < 2\).

Evaluate the Inequality for (2, 0)

Now, evaluating the inequality, it becomes 6 < 2, which is not true. Thus, (2,0) is not a solution for the given inequality.