R D Sharma Solutions for Chapter: Solution of Simultaneous Linear Equations, Exercise 1: EXERCISE

Solve the following system of equations by matrix method:

$5x+7y+2=0$, $4x+6y+3=0$

Solve the following system of equations by matrix method:

$5x+2y=3$, $3x+2y=5$

Show that each of the following systems of linear equations is consistent and also find their solutions:

$x+y+z=6$

$x+2y+3z=14$

$x+4y+7z=30$

Show that each of the following systems of linear equations is consistent and also find their solutions:

$2x+2y-2z=1$

$4x+4y-z=2$

$6x+6y+2z=3$

Two institutions decided to award their employees for the three values of resourcefulness, competence and determination in the form of prices at the rate of $₹ x, ₹ y$ and $₹ z$ respectively per person. The first institution decided to award respectively $4$, $3$ and $2$ employees with a total price money of $₹ 37000$and the second institution decided to award respectively $5$, $3$ and $4$ employees with a total price money of $₹ 47000$. If all the three prices per person together amount to $₹ 12000$then using matrix method find the value of $x, y$and $z$. What values are described in this equations?

Two factories decided to award their employees for three values of (a) adaptable to new techniques, (b) careful and alert in difficult situations and (c) keeping clam in tense situations, at the rate of $₹x, ₹y$ and $₹z$ per person respectively. The first factory decided to honour respectively $2$, $4$ and $3$ employees with a total prize money of$₹ 29000$. The second factory decided to honour respectively $5$, $2$ and $3$ employees with the prize money of $₹ 30500$. If the three prizes per person together cost $₹ 9500$, then

i) represent the above situation by matrix equation and form linear equation using matrix multiplication.

ii) Solve these equation by matrix method.

iii) Which values are reflected in the questions?

Two schools $P$ and $Q$ want to award their selected students on the values of Discipline, Politeness and Punctuality. The school $P$ wants to award $₹x$ each,$₹y$ each and $₹z$ each the three respectively values to its $3, 2$ and $1$ students with a total award money of $₹1,000$.School $Q$ wants to spend $₹ 1,500$ to award its $4, 1$and $3$ students on the respective values (by giving the same award money for three values as before). If the total amount of awards for one prize on each value is $₹ 600$, using matrices, find the award money for each value. Apart from the above three values, suggest one more value for awards.

A shopkeeper has $3$ varieties of pens$\text{'}A\text{'}, \text{'}B\text{'}$ and 'C'. Meenu purchased $1$ pen of each variety for a total of  $Rs 21$. Jeevan purchased $4$ pens of $\text{'}A\text{'}$ variety $3$ pens of $\text{'}B\text{'}$ variety and $2$ pens of $\text{'}C\text{'}$ variety for  $Rs 60$. While Shikha purchased $6$ pens of $\text{'}A\text{'}$ variety, $2$ pens of $\text{'}B\text{'}$ variety and $3$ pens of $\text{'}C\text{'}$ variety for  $Rs 70$. Using matrix method, find cost of each variety of pen.