69.3k views
5 votes
Which ordered pair is a solution tothe system of inequalities shown?

Which ordered pair is a solution tothe system of inequalities shown?-example-1
User Mkobit
by
7.5k points

1 Answer

2 votes

We want to know which ordered pair is a solution of the system of inequalities shown:


\begin{cases}x-4y\ge0 \\ x-y<-1\end{cases}

For doing so, we will try to solve both inequalities for one variable, in this case, we will use y.

On the first equation:


\begin{gathered} x-4y\ge0 \\ x\ge4y \\ y\le(x)/(4) \end{gathered}

On the second equation:


\begin{gathered} x-y<-1 \\ x+1-y<0 \\ x+1And joining those two results we get:[tex]x+1Now we check each of the ordered pairs, if they hold the condition above:<p><strong>For (0, 2)</strong></p><p>We have that x=0, and y=2. Thus, </p>[tex]\begin{gathered} x+1=1 \\ (x)/(4)=0 \\ \text{And as }2>0,\text{ (0, 2) is NOT a solution of the system.} \end{gathered}

For (-3, 8)

In this case, x=-3 and y=8.


\begin{gathered} x+1=-2 \\ (x)/(4)=-(3)/(4) \\ \text{As }8>-(3)/(4),\text{ this means that (-3, 8) is NOT a solution of the system.} \end{gathered}

For (2,5)

In this case, x=2 and y=5.


\begin{gathered} x+1=3 \\ (x)/(4)=(2)/(4)=(1)/(2) \\ \text{As }5>(1)/(2)\text{ this means that (2, 5) is NOT a solution of the system.} \end{gathered}

For (-7, -4)

In this case, x=-7 and y=-4.


\begin{gathered} x+1=-6 \\ (x)/(4)=-(7)/(4) \\ \text{As }-6<-4\le-(7)/(4),\text{ (-7, -4) is a SOLUTION of the system.} \end{gathered}

For (6, -1)

We have that x=6 and y=-1.


\begin{gathered} x+1=7 \\ (x)/(4)=(6)/(4)=(3)/(2) \\ \text{As }7>-1,\text{ (6, -1) is NOT a solution of the system. } \end{gathered}

Thus, the ordered pair which is a solution of the system is (-7, -4).

User Jacob Mason
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories