অনুশীলনী ৬.১

অষ্টম শ্রেণি (মাধ্যমিক)- গণিত - সরল সহসমীকরণ - অনুশীলনী ৬.১ | NCTB BOOK

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(ক)
প্রতিস্থাপন পদ্ধতিতে সমাধান কর (১–১২) :

(১)
x + y = 4
x - y = 2

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(২)
2x + y = 5
x - y = 1

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(৩)
3x + 2y = 10
x - y = 0

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(৪)
$\frac{x}{a} + \frac{y}{b} = \frac{1}{a} + \frac{1}{b}$
$\frac{x}{a} - \frac{y}{b} = \frac{1}{a} - \frac{1}{b}$

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(৫)
3x - 2y = 0
17x - 7y = 13

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(৬)
x - y = 2a
ax + by = a² + b²

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(৭)
ax + by = ab
bx + ay = ab

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(৮)
ax - by = ab
bx - ay = ab

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(৯)
ax - by = a - b
ax + by = a + b

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(১০)
$\frac{1}{x} + \frac{1}{y} = \frac{5}{6}$
$\frac{1}{x} - \frac{1}{y} = \frac{1}{6}$

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(১১)
$\frac{x}{a} + \frac{y}{b} = \frac{2}{a} + \frac{1}{b}$
$\frac{x}{b} - \frac{y}{a} = \frac{2}{b} - \frac{1}{a}$

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(১২)
$\frac{a}{x} + \frac{b}{y} = \frac{a}{2} + \frac{b}{3}$
$\frac{a}{x} - \frac{b}{y} = \frac{a}{2} - \frac{b}{3}$

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(খ)
অপনয়ন পদ্ধতিতে সমাধান কর (১৩-২৬) :

(১৩)
x - y = 4
x + y = 6

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(১৪)
2x + 3y = 7
6x - 7y = 5

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(১৫)
4x + 3y = 15
5x + 4y = 19

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(১৬)
3x - 2y = 5
2x + 3y = 12

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(১৭)
4x - 3y = -1
3x - 2y = 0

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(১৮)
3x - 5y = -9
5x - 3y = 1

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(১৯)
$\frac{x}{2} + \frac{y}{2} = 3$
$\frac{x}{2} - \frac{y}{2} = 1$

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(২০)
x + ay = b
ax - by = c

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(২১)
$\frac{x}{2} + \frac{y}{3} = 3$
$x - \frac{y}{3} = 3$

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(২২)
$\frac{x}{3} + \frac{2}{y} = 1$
$\frac{x}{4} - \frac{3}{y} = 3$

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(২৩)
$\frac{x}{a} + \frac{y}{b} = \frac{2}{a} + \frac{1}{b}$
$\frac{x}{b} - \frac{y}{a} = \frac{2}{b} - \frac{1}{a}$

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(২৪)
$\frac{a}{x} + \frac{b}{y} = \frac{a}{2} + \frac{b}{3}$
$\frac{a}{x} - \frac{b}{y} = \frac{a}{2} = \frac{b}{3}$

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(২৫)
$\frac{x}{6} + \frac{2}{y} = 2$
$\frac{x}{4} - \frac{1}{y} = 1$

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(২৬)
x + y = a - b
ax - by = a² + b²

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