Q 285 - Intermediate Algebra

Question

In the following exercise, determine whether each ordered pair is a solution to the system.   

$\left\{\begin{array}{l}6x-5y<20\\ -2x+7y>-8\end{array}\right.$

$$\begin{gathered} ⓐ (1, -3) \\ ⓑ (-4, 4) \end{gathered}$$

Step-by-Step Solution

Answer

Part (a).  The ordered pair $\left(1,-3\right)$ is not the solution to the given system of inequalities .

Part (b).  The ordered pair $(-4,4)$ is the solution to the given system of inequalities .

Part (a) Step 1. Substitute ( 1 , - 3 ) in the given system of inequalities.

Substituting $\left(1,-3\right)$ in the inequality

$6x - 5y < 20$:

$$\begin{gathered} 6x - 5y < 20 \\ 6\times 1-5\times (-3)<20 \\ 6+15<20 \\ 21<20 \end{gathered}$$

This is not true.

We need not to check further as it is not a solution.

Part (b) Step 1. Substitute - 4 , 4 in the given system of inequalities.

Substituting $\left(-4,4\right)$ in the inequality

$6x - 5y < 20$:

$$\begin{gathered} 6x - 5y < 20 \\ 6(-4)-5\left(4\right)<20 \\ -24-20<20 \\ -44<20 \end{gathered}$$

This is true.

Substituting $\left(-4,4\right)$ in the inequality

$-2x + 7y > -8$, we get:

$$\begin{gathered} -2x + 7y > -8 \\ -2(-4)+7\left(4\right)>-8 \\ 8+28>-8 \\ 36>-8 \end{gathered}$$

This is true.

Thus, the ordered pair $\left(-4,4\right)$ is the solution.