Solve- 4-9x-1-3y-1- 5x-2y-13

The correct option is C x=3, y= 1 Given system of equations are: 4/9x + 1/3y = 1 #160; ... (1) 5x+2y = 13 #160; ... (2)From equation 1 will ...

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Standard VIII

Mathematics

Eqns. reducible to pair of LE in 2 variables

Solve: 4/9x+...

Question

Solve:

$\frac{4}{9} x + \frac{1}{3} y = 1, 5 x + 2 y = 13$

x = 3, y = - 5

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x = 3, y = - 6

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x = 3, y = - 1

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x = 1, y = 0

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Solution

The correct option is C $x = 3, y = - 1$
Given system of equations are:
$\frac{4}{9} x + \frac{1}{3} y = 1$ ... (1)
$5 x + 2 y = 13$ ... (2)
From equation 1 will get:
$4 x + 3 y = 9$
Now subtracting eq1 and eq2
$4 x + 3 y = 9$
$5 x + 2 y = 13$
First multiply eq1 from 2 and eq2 from 2 will get:
$8 x + 6 y = 18$
$15 x + 6 y = 39$
now will subtract the equation
$\Rightarrow 8 x + 6 y = 18$
$- 15 x - 6 y = - 39$
$\Rightarrow - 7 x = - 21$
$\Rightarrow x = 3$
now substituting x = 3 in eq 2
$\Rightarrow 15 (3) + 6 y = 39$
$\Rightarrow 45 + 6 y = 39$
$\Rightarrow 6 y = 39 - 45$
$\Rightarrow 6 y = - 6$
$\Rightarrow y = - 1$
$\Rightarrow x = 3, y = - 1$

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Similar questions

Q. Solve the following systems of linear inequations graphically:

(i) 2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0
(ii) 2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
(iii) x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0
(iv) x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0
(v) 2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0

Q. Solve the following pairs of equations by reducing them to a pair of linear equations:

(i)

\frac{1}{2 x} + \frac{1}{3 y} = 2; \frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}

(ii)

\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = - 1

(iii)

\frac{4}{x} + 3 y = 14; \frac{3}{x} - 4 y = 23

(iv)

\frac{5}{x - 1} + \frac{1}{y - 2} = 2; \frac{6}{x - 1} - \frac{3}{y - 2} = 1

(v)

\frac{7 x - 2 y}{x y} = 5; \frac{8 x + 7 y}{x y} = 15

(vi)

6 x + 3 y = 6 x y; 2 x + 4 y = 5 x y

(vii)

\frac{10}{x + y} + \frac{2}{x - y} = 4; \frac{15}{x + y} - \frac{5}{x - y} = - 2

(viii)

\frac{1}{3 x + y} + \frac{1}{3 x - y} = \frac{3}{4}; \frac{1}{2 (3 x + y)} - \frac{1}{2 (3 x - y)} = \frac{- 1}{8}

Q. Solve the following simultaneous equations graphically.
(1) 2x + 3y = 12 ; x – y = 1
(2) x – 3y = 1 ; 3x – 2y + 4 = 0
(3) 5x – 6y + 30 = 0 ; 5x + 4y – 20 = 0
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Q. Solve:

\frac{2}{x} + \frac{3}{3 y} = \frac{1}{6}

and

\frac{3}{x} + \frac{2}{y} = 0

, where

x \neq 0; y \neq 0

Solve the following systems of linear inequations graphically :

$(i) 2 x + 3 y \leq 6, 3 x + 2 y \leq 6, x \geq 0, y \geq 0 (i i) 2 x + 3 y \leq 6, x + 4 y \leq 4, x \geq 0, y \geq 0 (i i i) x + y \geq 1, x + 2 y \leq 8, 2 x + y \geq 2, x \geq 0, y \geq 0 (i v) x + y \geq 1, 7 x + 9 y \leq 63, y \leq 5, x \geq 0, y \geq 0 (v) 2 x + 3 y \leq 35, y \geq 3, x \geq 2, x \geq 0, y \geq 0$

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Solve:49x+13y=1,5x+2y=13

Solve:

$\frac{4}{9} x + \frac{1}{3} y = 1, 5 x + 2 y = 13$