Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# Solve the following system of linear equations in three variables 1x-2y+4=0;1y-1z+1=0;2z+3x=14 - Mathematics

Sum

Solve the following system of linear equations in three variables

1/x - 2/y + 4 = 0; 1/y - 1/z + 1 = 0; 2/z + 3/x = 14

#### Solution

Let 1/x = p, 1/y = q and 1/z = r

p – 2q + 4 = 0

p – 2q = – 4   ...(1)

q – r + 1 = 0

q – r = – 1  ...(2)

3p + 2r = 14  ...(3)

(1) × 1 ⇒    p – 2q + 0 =  – 4  ...(1)
(2) × 2 ⇒    0 + 2q – 2r = – 2 ...(2)
(1) + (2) ⇒  p + 0  – 2r = – 6
p – 2r = – 6   ...(4)
(3) ⇒       3p + 2r = 14    ...(3)
(3) + (4) ⇒       4p + 0 = 8
4p = 8
p = 8/4 = 2

Substituting the value of p = 2 in (1)

2 – 2q = – 4

– 2q = – 4 – 2

– 2q = – 6

q = 6/2 = 3

Substituting the value of q = 3 in (2)

3 – r = 1

– r = – 1 – 3

r = 4

 But 1/x = p 1/x = 2 2x = 1  x = 1/2 1/y = q 1/y = 3 3y = 1 y = 1/3 1/z = r 1/z = 4 4y = 1 z = 1/4

The value of x = 1/2, y = 1/3 and z = 1/4

Is there an error in this question or solution?

#### APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 3 Algebra
Exercise 3.1 | Q 1. (ii) | Page 92