Question
Solve the following simultaneous equation graphically.
x – 3y = 1; 3x – 2y + 4 = 0
x – 3y = 1; 3x – 2y + 4 = 0
✓
Answer
The given simultaneous equations are
$x-3 y=1$
$\therefore \quad 3 y=x-1$
$\therefore \quad y=\frac{x-1}{3}$
$3 x-2 y+4=0$
$\therefore \quad 2 y=3 x+4$
$\therefore \quad y=\frac{3 x+4}{2}$
The two lines intersect at point (-2, -1).
∴ x = -2 and y = -1 is the solution of the simultaneous equations x – 3y = 1 and 3x – 2p + 4 = 0.
$x-3 y=1$
$\therefore \quad 3 y=x-1$
$\therefore \quad y=\frac{x-1}{3}$
| x | 4 | -2 | -5 | 1 |
| y | 1 | -1 | -2 | 0 |
| (x, y) | (4, 1) | (-2, -1) | (-5, -2) | (1, 0) |
$\therefore \quad 2 y=3 x+4$
$\therefore \quad y=\frac{3 x+4}{2}$
| x | 0 | -2 | 2 | -4 |
| y | 2 | -1 | 5 | -4 |
| (x, y) | (0, 2) | (-2, -1) | (2, 5) | (-4, -4) |
The two lines intersect at point (-2, -1).
∴ x = -2 and y = -1 is the solution of the simultaneous equations x – 3y = 1 and 3x – 2p + 4 = 0.
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
The following is the distribution of height of students of a certain class in a certain city:
|
Hight (in cms)
|
160-162
|
163-165
|
166-168
|
169-171
|
172-174
|
|
No. of students
|
15
|
118
|
142
|
127
|
18
|
In ΔABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C to side AB
To find number of notes that Anushka had, complete the following activity
ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that $\text{CQ}=\frac{1}{4}\text{AC}.$ If PQ produced meets BC at R, prove that R is the midpoint of BC.
→Find the height of an equilateral triangle of side 12cm.
The first term of an A.P. is p and its common difference is q. Find its $10^{th}$ term.
→Find the cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, -1 and -3 respectively.
Solve the following simultaneous equation graphically.
x – 3y = 1; 3x – 2y + 4 = 0
x – 3y = 1; 3x – 2y + 4 = 0
Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?
Seg AB and seg AD are the chords of the circle. C is a point on tangent of the circle at point A. If m(arc APB) 80° = and $\angle$BAD = 30°. Then find (i) $\angle$BAC (ii) m(arc BQD).
→