Question

19.x और y का मान ज्ञात करो
5x+ 9y= 30
6x+8y= 22
(a) x =-2,y=6​

Answer 1

$\underline{{ \fcolorbox{red}{pink}{ \huge{ \red{A}N\green{SW}E\red{R} :}}}}$

x = -3 and y = 5

$\underline{{ \fcolorbox{red}{pink}{ \huge{ \red{S}OL\green{UT}IO\red{N} : }}}}$

Given ,

The following pair of linear equations

$\sf \mapsto 5x + 9y = 30 \: ----- \: (i) \\ \\ \sf \mapsto 6x + 8y = 22 \: ----- \: (ii)$

Multiply eq (i) by 6 and eq (ii) by 5 , we get

(6)5x+ (6)9y = (6)30

30x + 54y = 180 ------- (iii)

&

(5)6x + (5)8y = (5)22

30x + 40y = 110 ------- (iv)

BY USING ELIMINATION METHOD

Subtract eq (iv) from eq (iii) , we get

$\mapsto \sf (30x + 54y) - (30x + 40y) = 180 - 110 \\ \\ \mapsto \sf</p><p>54y - 40y = 70 \\ \\ \mapsto \sf</p><p>14y = 70 \\ \\ \mapsto \sf</p><p>y = 70/14 \\ \\ \mapsto \sf</p><p>y = 5$

Put the value of y = 5 in eq (i) or eq (ii)

$\mapsto \sf 5x + 9(5) = 30 \: or \: 6x + 8(5) = 22 \\ \\ \mapsto \sf</p><p>5x + 45 = 30 \: or \: 6x + 40 = 22 \\ \\ \mapsto \sf </p><p>5x = - 15 \: or \: 6x = - 18 \\ \\ \mapsto \sf </p><p>x = -3 \: or \: x = -3$

Hence , the required values of x and y are -3 and 5