3.1 Systems of Linear Equations in Three Variables

3.1 Systems of Linear Equations in Three Variables - Set 2

Report 1 / 5

Determine the value of \(x, \, y \) and \(z\) that satisfy the following simultaneous linear equations:

\(\begin{aligned} 7x+6y+z&=9\quad &...\boxed{1} \\\\ 5x-4y-z&=2 \quad &...\boxed{2} \\\\ 8x+y+2z&=1 \quad &...\boxed{3} \end{aligned} \)

(A)		\(\begin{aligned} x&=\dfrac{29}{40} \\\\ y&=\dfrac{23}{20} \\\\ z&=\dfrac{119}{40} \end{aligned}\)

(B)		\(\begin{aligned} x&=\dfrac{29}{40} \\\\ y&=\dfrac{23}{20} \\\\ z&=-\dfrac{119}{40} \end{aligned}\)

(C)		\(\begin{aligned} x&=\dfrac{29}{40} \\\\ y&=-\dfrac{23}{20} \\\\ z&=\dfrac{119}{40} \end{aligned}\)

(D)		\(\begin{aligned} x&=-\dfrac{29}{40} \\\\ y&=\dfrac{23}{20} \\\\ z&=\dfrac{119}{40} \end{aligned}\)

Difficulty Level: Medium

3.1 Systems of Linear Equations in Three Variables - Set 2

Report 2 / 5

Find the solution for the following linear equation system.

\(\begin{aligned} 2x+y-z&=4 \\\\ x+2y+2z&=4 \\\\ -x+y+2z&=1 \end{aligned} \)

(A)		\(\begin{aligned} x&=0 \\\\ y&=3 \\\\ z&=1\end{aligned}\)

(B)		\(\begin{aligned} x&=0 \\\\ y&=3 \\\\ z&=-1\end{aligned}\)

(C)		\(\begin{aligned} x&=0 \\\\ y&=-3 \\\\ z&=1\end{aligned}\)

(D)		\(\begin{aligned} x&=0 \\\\ y&=-3 \\\\ z&=-1\end{aligned}\)

Difficulty Level: Medium

3.1 Systems of Linear Equations in Three Variables - Set 2

Report 3 / 5

The price of \(2\) curry puffs, a doughnut and \(3\) nuggets is \(\text{RM}3.00\) and the price of a curry puff, \(2\)
doughnuts and \(4\) nuggets is \(\text{RM}3.50\).

If a person buys \(3\) curry puffs, \(4\) doughnuts and a nugget, then he needs to pay \(\text{RM}4.50\).

Find the price of a curry puff, a doughnut and a nugget.

(A)		\(\begin{aligned} &\text{Price of a curry puff}&\hspace{-0.5cm}=&\,\text{RM}0.54\\\\ &\text{Price of a doughnut}&\hspace{-0.5cm}=\,&\text{RM}0.61\\\\ &\text{Price of a nugget}&\hspace{-0.5cm}=&\,\text{RM}1.43 \end{aligned}\)

(B)		\(\begin{aligned} &\text{Price of a curry puff}&\hspace{-0.5cm}=&\,\text{RM}0.54\\\\ &\text{Price of a doughnut}&\hspace{-0.5cm}=\,&\text{RM}1.61\\\\ &\text{Price of a nugget}&\hspace{-0.5cm}=&\,\text{RM}0.43 \end{aligned}\)

(C)		\(\begin{aligned} &\text{Price of a curry puff}&\hspace{-0.5cm}=&\,\text{RM}1.54\\\\ &\text{Price of a doughnut}&\hspace{-0.5cm}=\,&\text{RM}0.61\\\\ &\text{Price of a nugget}&\hspace{-0.5cm}=&\,\text{RM}0.43 \end{aligned}\)

(D)		\(\begin{aligned} &\text{Price of a curry puff}&\hspace{-0.5cm}=&\,\text{RM}0.54\\\\ &\text{Price of a doughnut}&\hspace{-0.5cm}=\,&\text{RM}0.61\\\\ &\text{Price of a nugget}&\hspace{-0.5cm}=&\,\text{RM}0.43 \end{aligned}\)

Difficulty Level: Medium

3.1 Systems of Linear Equations in Three Variables - Set 2

Report 4 / 5

A movie theatre charges \(\text{RM}16.00\) for adults, \(\text{RM}7.00\) for children and \(\text{RM}9.00\) for senior citizens.

On a particular day, the theatre sold \(260\) tickets and collected \(\text{RM}2\,550\) in receipts.

It is found that twice as many children's tickets were sold as adults tickets.

How many adults, children, and senior citizens watched movie in the theatre on that day?

(A)		\(\begin{aligned} &\text{Number of adults}&\hspace{-0.5cm}=&\,70\\\\ &\text{Number of children}&\hspace{-0.5cm}=\,&140\\\\ &\text{Number of senior citizens}&\hspace{-0.5cm}=&\,50 \end{aligned}\)

(B)		\(\begin{aligned} &\text{Number of adults}&\hspace{-0.5cm}=&\,75\\\\ &\text{Number of children}&\hspace{-0.5cm}=\,&120\\\\ &\text{Number of senior citizens}&\hspace{-0.5cm}=&\,55 \end{aligned}\)

(C)		\(\begin{aligned} &\text{Number of adults}&\hspace{-0.5cm}=&\,60\\\\ &\text{Number of children}&\hspace{-0.5cm}=\,&100\\\\ &\text{Number of senior citizens}&\hspace{-0.5cm}=&\,80 \end{aligned}\)

(D)		\(\begin{aligned} &\text{Number of adults}&\hspace{-0.5cm}=&\,70\\\\ &\text{Number of children}&\hspace{-0.5cm}=\,&80\\\\ &\text{Number of senior citizens}&\hspace{-0.5cm}=&\,40 \end{aligned}\)

Difficulty Level: Medium

3.1 Systems of Linear Equations in Three Variables - Set 2

Report 5 / 5

In a visit to an exhibition centre, group A which consists of \(3\) children, \(2\) teenagers and an adult paid a total entrance fee of \(\text{RM}90\).

Group B which consists of a child, \(3\) teenagers and \(2\) adults paid \(\text{RM}115\) while group C which consists of \(2\) children, a teenager and \(4\) adults paid \(\text{RM}140\).

Find the entrance fee for a child, a teenager and an adult.

(A)		\(\begin{aligned} &\text{Entrance fee for a child}&\hspace{-0.5cm}=&\,\text{RM}8.00\\\\ &\text{Entrance fee for a teenager}&\hspace{-0.5cm}=\,&\text{RM}20.00\\\\ &\text{Entrance fee for an adult}&\hspace{-0.5cm}=&\,\text{RM}25.80 \end{aligned}\)

(B)		\(\begin{aligned} &\text{Entrance fee for a child}&\hspace{-0.5cm}=&\,\text{RM}10.40\\\\ &\text{Entrance fee for a teenager}&\hspace{-0.5cm}=\,&\text{RM}18.00\\\\ &\text{Entrance fee for an adult}&\hspace{-0.5cm}=&\,\text{RM}25.00 \end{aligned}\)

(C)		\(\begin{aligned} &\text{Entrance fee for a child}&\hspace{-0.5cm}=&\,\text{RM}9.40\\\\ &\text{Entrance fee for a teenager}&\hspace{-0.5cm}=\,&\text{RM}18.00\\\\ &\text{Entrance fee for an adult}&\hspace{-0.5cm}=&\,\text{RM}25.80 \end{aligned}\)

(D)		\(\begin{aligned} &\text{Entrance fee for a child}&\hspace{-0.5cm}=&\,\text{RM}9.40\\\\ &\text{Entrance fee for a teenager}&\hspace{-0.5cm}=\,&\text{RM}18.00\\\\ &\text{Entrance fee for an adult}&\hspace{-0.5cm}=&\,\text{RM}35.00 \end{aligned}\)

Difficulty Level: Medium