Question
Represent the following pair of equations graphically and write the coordinates of points where the lines intersects y-axis.
x + 3y = 6,
2x - 3y = 12.
✓
Answer
The given equations are
x + 3y = 6 ......(i)
2x - 3y = 12 ........(ii)
Putting x = 0 in equation (i) we get,
⇒ 0 + 3y = 6
⇒ y = 2
⇒ x = 0, y = 2
Putting y = 0 in equation (i) we get,
⇒ x + 3 × 0 = 6
⇒ x = 6
⇒ x = 6, y = 0
Use the following table to draw the graph.
The graph of (i) can be obtained by plotting the two points A(0, 2), B(6, 0).
2x - 3y = 12 ......(ii)
Putting x = 0 in equation (ii) we get,
⇒ 2 × 0 - 3y = 12
⇒ y = -4
⇒ x = 0, y = -4
Putting y = 0 in equation (ii) we get,
⇒ 2x - 3 × 0 = 12
⇒ x = 6
⇒ x = 6, y = 0
Use the following table to draw the graph.
Draw the graph by plotting two points C(0, -4), D(6, 0) from table.
Graph of lines represented by the equations x + 3y = 6, 2x - 3y = 12 meet y-axis at A(0, 2), C(0, -4) respectively.
x + 3y = 6 ......(i)
2x - 3y = 12 ........(ii)
Putting x = 0 in equation (i) we get,
⇒ 0 + 3y = 6
⇒ y = 2
⇒ x = 0, y = 2
Putting y = 0 in equation (i) we get,
⇒ x + 3 × 0 = 6
⇒ x = 6
⇒ x = 6, y = 0
Use the following table to draw the graph.
|
x
|
0
|
6
|
|
y
|
2
|
0
|
2x - 3y = 12 ......(ii)
Putting x = 0 in equation (ii) we get,
⇒ 2 × 0 - 3y = 12
⇒ y = -4
⇒ x = 0, y = -4
Putting y = 0 in equation (ii) we get,
⇒ 2x - 3 × 0 = 12
⇒ x = 6
⇒ x = 6, y = 0
Use the following table to draw the graph.
|
x
|
0
|
6
|
|
y
|
-4
|
0
|
Graph of lines represented by the equations x + 3y = 6, 2x - 3y = 12 meet y-axis at A(0, 2), C(0, -4) respectively.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A chord AB of a circle, of radius 14cm makes an angle of 60° at the centre of the circle. Find the area of the minor segment of the circle.$\Big(\text{Use }\pi=\frac{22}{7}\Big)$
→Prove the following trigonometric identities.
$(1+\tan^2\text{A})+\Big(1+\frac{1}{\tan^2\text{A}}\Big)=\frac{1}{\sin^2\text{A}-\sin^4\text{A}}$
→$(1+\tan^2\text{A})+\Big(1+\frac{1}{\tan^2\text{A}}\Big)=\frac{1}{\sin^2\text{A}-\sin^4\text{A}}$
The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle of depression of the foot of the chimney forn the top of the tower is 30°. If the height of the tower is 40 metres, find the height of the chimney.
According to pollution control norms, the minimum height of a smokeemitting chimney should be 100 metres. State if the height ,the above mentioned chimney meets the pollution norms. What value is discussed in this question?
According to pollution control norms, the minimum height of a smokeemitting chimney should be 100 metres. State if the height ,the above mentioned chimney meets the pollution norms. What value is discussed in this question?
An express train takes $1$ hour less than a passenger train to travel $132\ km$ between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is $11\ km/hr$ more than that of the passenger train, find the average speed of two trains.
→→
Some students planned a picnic. The budget for food was $Rs. 500$. But, $5$ of them failed to go and thus the cost of food for each member increased by $Rs. 5$. How many students attended the picnic?
→Find the probability that a number selected at random from the numbers 1, 2, 3, ....., 35 is a:
- Prime number.
- Multiple of 7.
- A multiple of 3 or 5.
The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of:
- Heart.
- Queen.
- Clubs.
- A face card.
- A queen of diamond.
Each coefficient in equation $a x^2+b x+c=0$ is obtained by throwing an ordinary die. Find the probability that the equation has real roots.
→→