Question
Show graphically that the following system of equation is in-consistent (i.e. has no solution):
x - 2y = 6
3x - 6y = 0
✓
Answer
The given equations are,
x - 2y = 6 .......(i)
3x - 6y = 0 ........(ii)
From (i), $\text{y}=\frac{\text{x}-6}{2}\ ......(\text{iii})$
Putting x = 0 in (iii), we get y = -3
Putting x = 2 in (iii), we get y = -2
Putting x = 4 in (iii), we get y = -1
From (ii), $\text{y}=\frac{3\text{x}}{6}\ ......(\text{iv})$
Putting x = 0 in (iv), we get y = 0
Putting x = 2 in (iii), we get y = 1
Putting x = 4 in (iii), we get y = 2
When we plot these points on graph paper we observe that both linesare parallel to each other means they have no solution so they are in-consistent.
x - 2y = 6 .......(i)
3x - 6y = 0 ........(ii)
From (i), $\text{y}=\frac{\text{x}-6}{2}\ ......(\text{iii})$
Putting x = 0 in (iii), we get y = -3
Putting x = 2 in (iii), we get y = -2
Putting x = 4 in (iii), we get y = -1
|
x
|
0
|
2
|
4
|
|
y
|
-3
|
-2
|
-1
|
Putting x = 0 in (iv), we get y = 0
Putting x = 2 in (iii), we get y = 1
Putting x = 4 in (iii), we get y = 2
|
x
|
0
|
2
|
4
|
|
y
|
0
|
1
|
2
|
When we plot these points on graph paper we observe that both linesare parallel to each other means they have no solution so they are in-consistent.
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
|
Class interval
|
50-70
|
70-90
|
90-110
|
110-130
|
130-150
|
150-180
|
|
Frequency
|
18
|
12
|
13
|
27
|
8
|
22
|
The four vertices of a quadrilateral are (1, 2), (-5, 6), (7, -4) and (k, -2) taken in order. If the area of the quadrilateral is zero, find the value of k.
Following table shows frequency distribution of no. of rooms occupied in a hotel per day.
Find the median no. of rooms occupied in a hotel per day.
| No. of rooms occupied | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| No. of days | 5 | 27 | 17 | 11 | 9 | 1 |
$\triangle PQR \sim \triangle PAB , m \angle P =60^{\circ}, PQ =6 cm, PR =4 cm$. Construct $\triangle PAB$, if $PQ : PA =3: 2$.
→If $\cos\theta=\frac{12}{13},$ show that $\sin\theta(1-\tan\theta)=\frac{35}{156}.$
→There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
Find the mean, marks per stufdent, using assumed-mean method:
→|
Marks
|
$0-10$
|
$10-20$
|
$20-30$
|
$30-40$
|
$40-50$
|
$50-60$
|
|
Number of students
|
$12$
|
$18$
|
$27$
|
$20$
|
$17$
|
$6$
|
A cylindrical tube of radius $12\ cm$ contains water to a depth of $20\ cm.$ A spherical ball dropped into the tub and the level of the water is raised by $6.75\ cm$. Find the radius of the ball.
→Show that the points A(2, 1), B(5, 2), C(6, 4) and D(3, 3) are the angular points of a parallelogram. Is this figure a rectangle?
A missing helicopter is reported to have crashed somewhere in the rectangular region as shown in figure. What is the probability that it crashed inside the lake shown in the figure?
