Graphical Solution of Equations

Q.

If one root of the quadratic equation $2x^2-3x+p=0$ is 3. Find the other root of the quadratic equation. Also, find the value of $p$.

Q.

Rs 6500 were divided equally among a certain number of persons. Had there been 15 more persons, each would have got Rs 30 less. Find the original number of persons.

Q. Solve for x, 2/(x-1) is less than or equal to 3/(2x-3) using wavy curve method

Q.

If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4) then

1. $AP=\frac{1}{3}AB$

2. $AP=PB$

3. $PB=\frac{1}{3}AB$

4. $AP=\frac{1}{2}AB$

Q.

The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by x-axis is

1. 2:3

2. 7:4

3. 7:2

4. 3:1

Q.

A year ago, the father was 8 times as old as his son. Now, his age is the square of his sons age. Find their present ages.

Q.

Draw the graph of each of the following linear equations in two variables:

(i) (ii) (iii) y = 3x (iv) 3 = 2x + y

Q. Yamini and Fatima, two students of Class IX of a school, together contributed ₹ 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as ₹ x and ₹ y.) Draw the graph of the same.

Q.

The perpendicular distance of a point P from the X-axis is 4 units and from the Y-axis is 5 units (in the positive direction). What are the coordinates of point P?

1. P(4, 4)

2. P(5, 4)

3. P(4, 5)

4. P(5, 5)

Q.

The solution of the equations $\frac{3x-y+1}{3}=\frac{2x+y+2}{5}=\frac{3x+2y+1}{6}$ is given by:

1. $x=2,y=1$

2. $x=1,y=1$

3. $x=-1,y=-1$

4. $x=1,y=2$

Q.

A two-digit number is 5 times the sum of its digits and is also equal to 5 more than twice the product of its digits. Find the number.

Q. Write two solutions of the form x = 0, y = a and x = b, y = 0 for each of the following equations:

(i) 5x − 2y = 10

(ii) −4x + 3y = 12

(iii) 2x + 3y =24

Q.

On solving $\frac{25}{x+y}-\frac{3}{x-y}=1,\frac{40}{x+y}+\frac{2}{x-y}=5$ we get:

1. $x=8,y=6$

2. $x=4,y=6$

3. $x=6,y=4$

4. None of these.

Q. Match the equations with their solutions.

1. (2, 2)
2. (1, 2)
3. (-1, 1)

Q.

The sum of the numerator and denominator of a certain fraction is $11$. If $1$ is added to both numerator and denominator, the fraction increases by $\frac{3}{56}$. Find the fraction.

Q. Minimum points required to draw a straight line are ______.

1. 0
2. 4
3. 2
4. 3

Q. How many solutions can the equation 5x + 4y = 2 have?

1. Data inadequate
2. Infinite
3. One
4. Two

Q.

A point lying on a line should satisfy the equation of the line.

1. True
2. False

Q.

1. By which, either an ordered pair or an integer, a solution of a linear equation in two variables is always given?

2. Is it true that the graph of the linear equations X + 2 Y equal to 7 passes through the point (0, 7)?

Q.

If (x-1, y +3) = (7, -7), then find the values of x and y respectively.

1. 8, -10

2. 6, -4

3. 8, 10

4. -8, -10

Q. If 3a+2b+4c=0, then show that the equation ax+by+c=0 represents a family of concurrent straight lines and find the point of concurrency.

Q.

In what ratio does the X-axis divide the line segment joining the points (-4, -6) and (-1, 7)? Find the coordinates of the points of division.

1. $(\frac{-32}{15},0)$.

2. $(\frac{-34}{13},0)$.

3. $(\frac{-30}{13},0)$.

4. $(\frac{-34}{12},1)$.

Q.

Some students planned a picnic. The budget for food was Rs $480$. But $4$ of these failed to go and thus the cost of food for each member increased by Rs $10$. How many students attended the picnic ?

Q.

Find the value of $p$; if one root of the quadratic equation $3x^2-px-6=0$ is $3$. Also, find the second (other) root of the equation.

Q.

If the point P(5, k-2) lies on the line $x-2y+1=0$, then find the value of k.

1. 5

2. 6

3. 4

4. 3

Q.

A piece of cloth costs Rs 35. If the piece was 4 m longer and each metre cost Rs 1 less, the cost would remain unchanged. How long is the piece?

Q.

The inclination of the line AB in the given figure is ___

1. ${30}^{\circ }$

2. ${45}^{\circ }$

3. ${60}^{\circ }$

4. ${90}^{\circ }$

Q. Graph of the equation $2x+3y=9$ cuts y - axis at the point :

1. $(\frac{9}{2},0)$
2. $(0,9)$
3. $(0,3)$
4. $(3,1)$

Q. The taxi fare in a city is as follows: For the first kilometre, the fare is Rs. 8 and for the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total fare as Rs. y, write a linear equation for this information, and draw its graph.

Q.

The reason for the equations $x+2y=5$ and $4x+8y=20$ to have infinite solutions is :

1. The graph of the system of equations meets at infinity

2. The graph reaches infinity

3. The graph of both the equations is the same line

4. none of these