# Graphical Solution of Equations

## Trending Questions

**Q.**

If one root of the quadratic equation $2{x}^{2}-3x+p=0$ 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

AP=13AB

AP=PB

PB=13AB

AP=12AB

**Q.**

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

2:3

7:4

7:2

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* = 3*x *(iv) 3 = 2*x* + *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?

P(4, 4)

P(5, 4)

P(4, 5)

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:

$x=2,y=1$

$x=1,y=1$

$x=-1,y=-1$

$x=1,y=2$

**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:

$x=8,y=6$

$x=4,y=6$

$x=6,y=4$

None of these.

**Q.**Match the equations with their solutions.

- (2, 2)
- (1, 2)
- (-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 ______.

- 0
- 4
- 2
- 3

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

- Data inadequate
- Infinite
- One
- Two

**Q.**

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

- True
- 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.

8, -10

6, -4

8, 10

-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.

(−3215, 0).

(−3413, 0).

(−3013, 0).

(−3412, 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 $3{x}^{2}-px-6=0$ 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.

5

6

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

30∘

45∘

60∘

90∘

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

- (92, 0)
- (0, 9)
- (0, 3)
- (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 :

The graph of the system of equations meets at infinity

The graph reaches infinity

The graph of both the equations is the same line

none of these