Problems Reducible to Simultaneous Equations

Q.

$\frac{x+y-8}{2}$ = $\frac{x+2y-14}{8}$ = $\frac{3x+y-12}{11}$
Solve the given system of equations:

1. (1, -1)

2. (2, 6)

3. (2, 2)

4. (0, 1)

Q.

The cost of a room in a hotel is partially fixed and partially varying with the number of hours. A person staying for 10 hours paid Rs. 600 and a person staying for 15 hours paid Rs. 840. Find the fixed cost and the variable cost per hour.

1. Rs. 120, Rs. 48/hr

2. Rs. 120, Rs. 100/hr

3. Rs. 200, Rs. 120/hr

4. Rs. 200, Rs. 48/hr

Q.

Find the values of $x$ and $y$ that satisfy both the given equations.
$y-2x=4$ and $y-3x=2$

1. $(2,4)$

2. $(4,2)$

3. $(8,1)$

4. $(2,8)$

Q. What are the points where line $x+2y=4$ cuts the x-axis and y-axis?

1. (4, 0)
2. (2, 1)
3. (0, 2)
4. (1, 1)

Q. In a certain code, BAT =23 and CAT = 24, then how will you code BALL?

1. 32
2. 28
3. 120
4. 27

Q.

Question 4 (v)
Find the values of p and q for the following pair of equations 2x + 3y = 7 and 2px + py = 28 – qy, if the pair of equations has infinitely many solutions.

Q. Question 1 (ii)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

Q. Question 2 (ii)
Formulate the following problems as a pair of equations, and hence find their solutions:
2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

Q.

A square is formed by reducing the length of a rectangle by 4 cm and increasing it's width by 3 cm. Both the figures have the same area. Find the perimeter of the original rectangle.

1. 48 cm

2. 50 cm

3. 40 cm

4. None of these

Q. Solve the following pairs of equations by reducing them to a pair of linear equations:
6x + 3y = 6xy
2x + 4y = 5xy

Q. is a solution of the equation $y=6x+2.$

1. $(1,8)$
2. $(0,1)$
3. $(2,0)$
4. $(-1,2)$

Q.

Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}$
$\frac{1}{2(3x+y)}-\frac{1}{2(3x-y)}=\frac{-1}{8}$

1. (2, 1)

2. (1, -1)

3. (3, 2)

4. (1, 1)

Q. Question 2 (iii)
Formulate the following problems as a pair of equations, and hence find their solutions:
Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Q.

The cost of a room in a hotel is partially fixed and partially varying with the hours stayed. A person staying for 10 hours paid ₹ 600 and a person staying for 15 hours paid ₹ 840. Find the algebraic expression representing this situation.

1. $x+10y=840;x+15y=600$

2. $x+10y=600;x+15y=840$

3. $10x+15y=600;15x+10y=840$

4. $10x=600;15y=840$

Q. Question 4
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

Q. If the point (1, 3) lies on the line $x+ky=4$, then k is.

1. 1
2. 2
3. 3
4. 4

Q.

Q. What are the lines passing through the point (1, 1)?

1. $x=y$
2. $x+3y=4$
3. $x+4y=9$
4. $4x-2y=2$

Q. A worm starts moving 5 units from the origin towards the positive x - axis and then it moves 6 units towards the negative y - axis and then it moves 8 units towards the negative x - axis to complete its journey. What will be the coordinates of the worm after it completes its journey?

Q. What are the possible solutions for the equation $x+2y=10$?

1. $x=0$ and $y=5$
2. $x=10$ and $y=0$
3. $x=5$ and $y=5$
4. $x=4$ and $y=3$

Q. What's the equation of the line passing through the points (0, 0), (1, 1) and (2, 2)?

1. $y=x$
2. $y=2x+1$
3. $y=4x+4$
4. $y=2x$

Q.

Half the perimeter of a rectangular garden whose length is 4 m more than its width is 36 m. Find the dimensions of the garden.

1. Length = 20 m, breadth = 16 m

2. Length = 24 m, breadth = 20 m

3. Length = 40 m, breadth = 36 m

4. Length = 20 m, breadth = 18 m

Q. Line $y=4$ is parallel to .

1. $x-axis$
2. $y-axis$
3. $x=4$
4. $x=6$

Q.

The cost of a room in a hotel is partially fixed and partially varying with the hours stayed. A person staying for 10 hours paid ₹ 600 and a person staying for 15 hours paid ₹ 840. Find the algebraic expression representing this situation.

1. $10x+15y=600;15x+10y=840$

2. $x+10y=600;x+15y=840$

3. $x+10y=840;x+15y=600$

4. $10x=600;15y=840$

Q. Half the perimeter of a rectangular garden, whose length is 4 m more than it's breadth, is 16 m, then the dimensions of the garden are .

1. $10m\&6m$
2. $12m\&4m$
3. $11m\&5m$
4. $9m\&7m$

Q.

If you have two lawns - one in front of your house and the other at the back, in the shape of a rectangle, find the perimeter if its lengths and breadth s are given as follows:
i. l = 10 cm, b = 8 cm
ii. l = 18 cm, b = 12 cm

1. i. 36 cm, ii. 60 cm

2. i. 40 cm, ii. 56 cm

3. i. 34 cm, ii. 64 cm

4. i. 30 cm, ii. 40 cm

Q.

The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Reduce these statements in the form of linear equations assuming number of rows to be 'x' and number of students in a row to be 'y'.

1. $x-y=3$

   $3x+2y=5$

2. $3x-y=3$

   $3x-2y=-6$

3. None of the above

4. $-3x+y=-2$

   $x-2y=6$

Q.

A rectangular box has a height $hcm$. Its length is$5times$ its height and its breadth is $10cm$ less than its length. Express the length and breadth in terms of the height.

Q. Draw a graph of equation $2x+5y=1$. Write the coordinates of the points where the lines meets two axes.

1. 0.4, 0.2
2. 0.5, 0.2
3. 0.2, 0.5
4. 0.2, 0.4

Q. The cost of a room in a hotel is partially fixed and partially varying with the number of hours. A person staying for 10 hours paid Rs. 600 and a person staying for 15 hours paid Rs. 840. Find the fixed cost and the variable cost per hour.