Framing Algebraic Equations

Q. If the pair of linear equations $x+2y-4=0$ and $2x+4y-12=0$ are plotted graphically, we get solution(s).

1. Infinite
2. Unique
3. zero

Q.

Express the linear equations $5=2x$ in the form $ax+by+c=0$ and indicate the values of $a,b$ and $c$.

Q. "The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. How many pants were purchased?

1. 1

Q. Ravish tells his daughter Aarushi, Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.

Q. The sum of two angles of a triangle is 116 and their difference is 24. Find the measure of each angle of the triangle.

Q.

A father tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Select the algebraic equations that represent this situation.

1. $x–7y=-42$

2. $x–3y=6$

3. $7x–2y=-32$

4. $x+3y=-6$

Q.

Geeta’s age is 3 years more than thrice m, the age of Meeta. Write an equation of first degree to display this information.

1. g - 3 = 3m

2. g + 3 = 3m

3. g - 3m + 3 = 0

4. g + 3m + 3 = 0

Q. Question 102(i)
Using suitable rearrangement, find the sum.
$\frac{4}{7}+\left(\frac{-4}{9}\right)+\frac{3}{7}+\left(\frac{-13}{9}\right)$

Q. If the point (3, 5) lies on the graph of the equation 3y = ax + 9, then the value of a is :

1. 2

Q.

Express the linear equations $x=3y$ in the form $ax+by+c=0$ and indicate the values of $a,b$ and $c$.

Q. Question. The perimeter of a rectangle is 240 cm. If its length is decreased by 10% and breadth is increased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.

Q. The cost of a ball pen is ₹5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.

1. 2x – y + 10 = 0
2. x + 9y + 14 = 0
3. x + 2y + 10 = 0
4. x + y = 5

Q. Which of the following correctly represents when b = 0 in the standard equation ax + by + c = 0

1. by + c = 0
2. ax + c = 0
3. ax + by + c = 0
4. None of the above

Q.

The cost of 3 cricket bats and 6 balls is ₹ 3900. The cost of one bat and 3 balls of the same kind is ₹ 1700. Select the equations that represent this situation algebraically.

1. $x-2y=1300$

2. $x+2y=1300$

3. $3x+2y=1700$

4. $x+3y=1700$

Q. Find the three integral solutions of 3x+4y+24=0 reptesent this equation by graph

Q.

What is the solution for the equation: $4x-\frac{1}{3}=1?$

1. $x=\frac{2}{3}$

2. $x=2$

3. $x=\frac{4}{3}$

4. $x=\frac{1}{3}$

Q.

An aeroplane flies 16 km/h with a head wind in 3.5 hours . On return trip with same wind blowing , the plane takes 3 hours .

Q.

Write the following statement as an equation.
The number of students in my class is 46, which is six less than four times the number of the benches in my class. (Assume that the number of benches is x.)

1. 4x + 6 = 46

2. 6x + 4 = 46

3. 6x - 4 = 46

4. 4x - 6 = 46

Q. What is the value of x if the pair of linear equation $x+3y=6$ and $2x-3y=12$ intersect at a point?

1. 6

Q.

Express this statement as an equation:
My age is 3 years less than twice the age of my brother. Assume that my brother’s age is x and my age is y.

1. x - 2y = 3

2. 2x + y = 3

3. 2x - y = 3

4. 3x - 2y = 0

Q. Ram has $x$ pens and Mohan has 5 pens more than the pens that Ram has. Then, the total number of pens Mohan has is.

1. $x$ + 5
2. $x$
3. $x$ - 5
4. 5$x$

Q. If 4x + 3y = 126 (x ≥ y) and x, y are positive integers, then the number of possible solutions of (x, y) is

यदि 4x + 3y = 126 (x ≥ y) तथा x, y धनात्मक पूर्णांक हैं, तब (x, y) के संभावित हलों की संख्या है

1. 4
2. 5
3. 6
4. 7

Q.

The difference between two numbers is 70. The numbers are in ratio 5:3. Let the numbers be x and y (x > y). Select the correct equations.

1. $x-y=70$

2. $x+y=35$

3. $3x-5y=0$

4. $5x-3y=0$

Q. The sum of four times of Keerthi's age and twice the age of her brother Shankar is 64. Choose the equation(s) that represent(s) the following situation accordingly.
(Assume Keerthi's age to be '$x$' and Shankar's age to be '$y$'.)

1. $4x+2y=64$
2. $2x+y=32$
3. $2x+4y=64$
4. $x+2y=32$

Q. The total number of non-negative integer solutions possible for the equation
x + y = 2 is .

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

Q. My friend has 4 more than twice the number of chocolates I have. How many chocolates does he have if I have a total of $25$ chocolates.

1. 54

Q.

1. x+2y=0

2. x+y=0

Q. In a rectangle, length is twice the breadth. If the length of a rectangle is increased by 20% and its breadth is increased by 10%. The percentage increase in its perimeter will be :

Q.

x = 7, y = 3 satisfies which of the following equations?

1. x + y = 7

2. x + y = 4

3. x + 3y = 16

4. x - y + 4 = 0

Q.

If the ordinate (value of the '$y$' coordinate) is twice the abscissa (value of the '$x$' coordinate), then find the point where $7x-3y=8$.

1. (8, 16)

2. (2, 4)

3. (3, 6)

4. (6, 3)