Match the following if x-2-y-1-2-3 and x-1-y-2-1-3

The correct option is ∴ x + 2 /y 1 = 2/3 and x + 1 nbsp;/y + 2 = 1/3 ⇒ 3x 2y = 8 ....(i) and 3x y = 1......(ii) ⇒3x 2y = 8 ( 3x y = 1) ⇒ ...

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Standard IX

Mathematics

Solving Equations Using Method of Substitution

Match the fol...

Question

Match the following if $\frac{x + 2}{y - 1} = \frac{2}{3} a n d \frac{x + 1}{y + 2} = \frac{1}{3}$

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\frac{2}{7}

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\frac{7}{2}

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Solution

$∴ \frac{x + 2}{y - 1} = \frac{2}{3} a n d \frac{x + 1}{y + 2} = \frac{1}{3}$

$\Rightarrow 3 x - 2 y = - 8 . . . . (i)$
$a n d 3 x - y = - 1...... (i i)$

$\Rightarrow 3 x - 2 y = - 8$
$- (3 x - y = - 1)$

$\Rightarrow 3 x - 2 y = - 8$
$- 3 x + y = 1$

$- y = - 7$

$\Rightarrow y = 7$

Substituting y = 7 in equation (ii), we get
$3 x - (14) = - 8$
$3 x = - 8 + 14 = 6$
$∴ x = 2$

$\Rightarrow x = 2 a n d y = 7$

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Q. If

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and

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then the value of

\frac{x_{1}^{2}}{x_{1}^{2} + x_{2}^{2} + x_{3}^{2}} + \frac{y_{1}^{2}}{y_{1}^{2} + y_{2}^{2} + y_{3}^{2}}

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(correct answer + 2, wrong answer - 0.50)

Q. If the points

(x_{1}, y_{1}), (x_{2}, y_{2})

and

(x_{3}, y_{3})

are collinear, show that

\sum (\frac{y_{1} - y_{2}}{x_{1} x_{2}}) = 0,

i.e

\frac{y_{1} - y_{2}}{x_{1} x_{2}} + \frac{y_{2} - y_{3}}{x_{2} x_{3}} + \frac{y_{3} - y_{1}}{x_{3} x_{1}} = 0

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Match the following if x+2y−1=23 and x+1y+2=13

∴ x+2y−1=23 and x+1y+2=13 ⇒ 3x−2y=−8....(i) and 3x−y=−1......(ii) ⇒3x−2y=−8 −(3x−y=−1) ⇒3x−2y=−8 −3x+y=1 ______________________ −y=−7 ______________________ ⇒y=7 Substituting y = 7 in equation (ii), we get 3x−(14)=−8 3x=−8+14=6 ∴x=2 ⇒x=2 and y=7

Match the following if $\frac{x + 2}{y - 1} = \frac{2}{3} a n d \frac{x + 1}{y + 2} = \frac{1}{3}$