Telangana SCERT Solution Class X (10) Maths Chapter 4 Pair of linear equations in two variables Exercise 4.3
Pair of linear equations in two variables
Exercise – 4.3
P = 1/3
Substitute p = 1/3 in equation (3), we get,
5 X 1/3 + q = 2
5/3 + q = 2
Q = 2 – 5/3
Q = 6-5/3
Q = 1/3
But p = 1/x-1 and q = 1/y-2
1/3 = 1/x-1
(x – 1) = 3
X – 1 = 3
X = 3 + 1
X = 4
1/3 = 1/y-2
(y – 2) = 3
Y – 2 = 3
Y = 3+2
Y = 5
Q = 8/2
Q = 4
Substitute q = 4 in equation (3), we get.
P + 4 = 2
P = 2 – 4
P = – 2
But 1/x = p and 1/y = q,
1/x = -2 and 1/y = +4
X = -1/2 and y = 1/4 (Take reciprocal on both sides)
Substitute q = 1/3 in equation (3), we get
2p + 3 X 1/3 = 2
2p + 1 = 2
2p = 2 – 1
2p = 1
P = 1/2
But p = 1/√x and q = 1/√y
1/2 = 1/√x
√x = 2
q = 1/√y
1/3 = 1/√y
Squaring on both side √y = 3
(√x)2 = (2)2
(√x)2 4
X = 4
(√y)2 = (3)2
Y = 9
(iv) 6x + 3y = 6xy, 2x + 4y = 5xy
=> Solution: Given paires of equation.
6x + 3y = 6xy
Divide xy on both side,
6x/xy + 3y/xy = 6xy/xy
6/y + 3/x = 6
6 (1/y) + 3 (1/x) = 6 —— (1)
2x + 4y = 5xy
Divide xy on both side,
2x/xy + 4y/xy = 5xy/xy
2/y + 4/x = 5
2 (1/y) + 4 (1/x) = 5 —— (2)
Substitute 1/x = p and 1/y =q, we get
6q + 3p = 6 —— (3)
2q + 4p = 5 —— (4)
(v) 5/x+y – 2/x-y = -1, 15/x+y + 7/x-y = 10
=> Solution: Given pairs of equations are,
5 (1/x+y) – 2 (1/x-y) = -1 —— (1)
15(1/x+y) +7 (1/x-y) = 10 ——– (2)
Substitute 1/x+y = p and 1/x-y = q,
5p – 2q = -1 ——- (3)
15p + 7q = 10 ——- (4)
Multiply equation (3) by (3), we get
3 X 5p – 2 X 3q = – 1 X 3
15p – 6q = – 3 —— (5)
Substitute x = 3 in equation (6), we get
3 + y = 5
Y = 5 – 3
Y = 2
Substitute p = 2 in equation (3), we get
2 X 2 + 3q = 13
4 + 3q = 13
3q = 13 – 4
3q = 9
q = 3
But p = 1/x and q = 1/y
2 = 1/x
x = 1/2
3 = 1/y
Y = 1/3
(vii) 10/x+y + 2/x-y = 4, 15/x+y – 5/x-y = -2
=> Solution: Given pairs of equation,
10 (1/x+y) +2 (1/x-y) = 4 —– (1)
15 (1/x+y) – 5 (1/x+y) = – 2 —– (2)
Substitute 1/x+y = p and 1/x-y = q, we get
10p + 2q = 4 —— (3)
15p – 5q = – 2 ——– (4)
y = 4 – 3
y = 1
(Q2) Formulate the following problems as a pair of equations and then find their solutions.
(i) A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40 km upstream and 55 km downstream. Determin the speed of the stream and that of the boat in still water
=> Solution:
Let beat speed be x and the stream speed be y.
From first condition,
By using formula,
Speed = distance/time
Time = distance/speed
10 = 30/x-y + 44/x+y —– (1)
∵ boat → x → boat x
River → y ← river y
Downstream upstream
(+) (-)
(ii) Rahim travels 600 km to his home partly by train and parly by car. He takes 8 hours if he travels 120 km by train and rest by car. He takes 20 minutes more if he travels 200 km by train and rest by car. Find the speed of the train and the car.
=> Solution:
Let the speed of train = x km/hr and the speed of the car = y km/hr.
By formula,
S = d/t
T = d/s
From first condition,
He takes 8 hours if he travels 120 km by train and rest by car.
8 = 120/x + 480/y —– (1) [∵ 600 – 120 = 480]
From second condition:
He takes 20 minutes more if he travels 200 km by train and rest by car.
8 + 20/60
= 24+1/3
= 25/3
Substitute q = 1/80 in equ∩ (3), we get
120p + 480 X 1/80 = 8
120p + 6 = 8
120 = 8 – 6
120p = 2
P = 2/120
P = 1/60
But 1/x = p and 1/y = q, we get.
1/x = 1/60 and 1/y = 1/80
X = 60 and y = 80
∴ The speed of train = 60 km/hr and the sped of train = 80 km/hr
.
(iii) 2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days. Find the time to taken by 1 women alone and 1 man alone to finish the work.
=> Solution:
Let one man finish work in x days and one women finish work in y days.
∴ One man 1 day work = 1/x
And one women 1 day work = 1/y
From first condition,
2 women and 5 men can together finish an embroidery work in 4 days.
2X1/y + 5X1/x = 1/4 —- (1)
From second condition:
3 women and 6 men can finish it in 3 days.
3X1/y + 6X1/x = 1/3 —– (2)
Substitute 1/x = q and 1/y = p, we get.
2p + 5q = 1/4 —– (3)
q = 1/36
Substitute q = 1/36 in equation (4), we get.
3p + 6X1/36 = 1/3
3p + 6/36 = 1/3
3p = 1/3 – 1/6
3p = 6-3/18
3p = 3/18
3p = 1/6
P = 1/3X6
P = 1/18
But p = 1/y and q = 1/x, we get.
1/18 = 1/y
Y = 18
1/36 = 1/x
X = 36
∴ The time to taken by 1 women alone = 18 days
And the time to taken by 1 man alone = 36 days
Here is your solution of Telangana SCERT Class 10 Math Chapter 4 Pair of linear equations in two variables Exercise 4.3
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