Q.(a) Find the value of x and y in the equations by using Cramer's rule x+3y=1 and 3x-2y=14.

(a) By Cramer's rule the solution of x + 3y = 1 and 3x − 2y = 14 is x = 4, y = −1. (b) Large Scale Industries are capital- and technology-intensive units producing on a mass scale (steel, textiles, cement, automobiles), important for industrialisation, employment and growth.

(a) Solve by Cramer's Rule (shown step by step in plain notation, no special symbols)

Given equations:

• x + 3y = 1
• 3x − 2y = 14

Step 1 — Write the coefficient determinant D (coefficients of x and y):

D = | 1 3 |

| 3 −2 |

D = (1)(−2) − (3)(3) = −2 − 9 = −11

Since D is not equal to 0, a unique solution exists.

Step 2 — Form Dx (replace the x-column with the constants 1 and 14):

Dx = | 1 3 |

| 14 −2 |

Dx = (1)(−2) − (3)(14) = −2 − 42 = −44

Step 3 — Form Dy (replace the y-column with the constants 1 and 14):

Dy = | 1 1 |

| 3 14 |

Dy = (1)(14) − (1)(3) = 14 − 3 = 11

Step 4 — Apply Cramer's rule:

x = Dx / D = (−44) / (−11) = 4

y = Dy / D = (11) / (−11) = −1

Step 5 — Verification:

• Equation 1: x + 3y = 4 + 3(−1) = 4 − 3 = 1 (correct)
• Equation 2: 3x − 2y = 3(4) − 2(−1) = 12 + 2 = 14 (correct)

Hence x = 4 and y = −1.

(b) Large Scale Industries

Meaning. Large Scale Industries are industries that are organised on a large scale, employing heavy capital, large amounts of machinery, big workforces and large quantities of raw materials to produce goods in mass quantities. (In India, scale is broadly judged by the size of investment in plant and machinery.)

Features:

1. Large capital investment in fixed assets, plant and machinery.
2. Mass production of standardised goods using modern technology.
3. Large workforce and specialised, divided labour.
4. Wide market, often national and international.
5. Economies of scale — lower cost per unit as output rises. …