Q. 281 - Intermediate Algebra

Question

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

$\left\{\begin{array}{l}4x- y< 10\\ -2x+ 2y -8\end{array}\right.$

$$\begin{gathered} ⓐ (5, -2) \\ ⓑ (-1, 3) \end{gathered}$$

Step-by-Step Solution

Answer

Part (a). The ordered pair $(5,2)$ is not the solution of the given system of inequalities.

Part (b). The ordered pair $\left(-1,3\right)$ is the the solution of the given system of inequalities.

Part (a) Step 1. Substitute 5 , - 2 in the given system of inequalities.

Substituting $$\begin{gathered} x=5 \\ y=-2 \end{gathered}$$ in the inequality

$4x-y<10$:

$$\begin{gathered} 4x-y<10 \\ 4\left(5\right)-(-2)<10 \\ 20+4<10 \\ 24<10 \end{gathered}$$

This is not true.

Substituting $$\begin{gathered} x=5 \\ y=-2 \end{gathered}$$ in the inequality

$-2x+2y>-8$:

This is also not true.

Thus, the ordered pair is not a solution.

Part (b) step 1. Substitute - 1 , 3 in the given system of inequalities.

Substituting $$\begin{gathered} x=-1 \\ y=3 \end{gathered}$$ in the inequality

:

$$\begin{gathered} 4x-y<10 \\ 4(-1)+3<10 \\ -4+1<10 \\ -3<10 \end{gathered}$$

This is true.

Substituting $$\begin{gathered} x=-1 \\ y=3 \end{gathered}$$ in the inequality

$-2x + 2y > -8$:

$$\begin{gathered} -2x + 2y > -8 \\ -2(-1)+2\left(3\right)>-8 \\ 2+6>-8 \\ 8>-8 \end{gathered}$$

This is true.

So, the ordered pair $\left(-1,3\right)$ is the solution.