Mathematics — Standard (041) — CBSE Class 10 board question

Elimination Method:

Given: $30x + 44y = 10$ … (1) and $40x + 55y = 13$ … (2)

Multiply (1) by 4 and (2) by 3:

$120x + 176y = 40$ … (3)

$120x + 165y = 39$ … (4)

Subtract (4) from (3):

$11y = 1 \Rightarrow y = \dfrac{1}{11}$

Substitute in (1): $30x + 44 \times \dfrac{1}{11} = 10$

$30x + 4 = 10 \Rightarrow 30x = 6 \Rightarrow x = \dfrac{1}{5}$

$\therefore x = \dfrac{1}{5},\quad y = \dfrac{1}{11}$

Source: Chapter 3, Section 3.3.2 (Elimination Method)

• Make coefficients of one variable equal by multiplying both equations by suitable numbers, then subtract to eliminate that variable.
• After finding one variable, substitute back into either original equation.
• Examiners award marks for: correct multiplication step, correct subtraction, correct value of each variable.