Question

5x- 4y + 8 = 0
7x+6y-9 = 0​

Answer 1

Answer:

x= -6/29

y= 101/58

Step-by-step explanation:

5x-4y= -8 -(i) ×3

7x+6y= 9 -(ii) ×2

The equations becomes,

15x-12y= -24 -(i)

14x+12y= 18 -(ii)

Adding (i) and (ii),

15x-12y= -24

14x+12y= 18

__________

29x = -6

=> x = -6/29

And,

5x-4y =-8 (i)

=> 5×-6/29 -4y= -8

=> -4y = -8 + 30/29

=> -4y = (-232 +30)/29

=> -4y = -202/29

=> -y = -202/29×4

=> -y = -101/58

=> y =101/58

Answer 2

Answer:

$\green{ \large \rm \: GIVEN \: \: \: EQUATIONs } \pink{ \rightarrow}$

$\sf \: 5x- 4y + 8 = 0 \: \: \: \: \: \: \: ............(i) \\ \sf7x + 6y - 9 = 0 \: \: \: \: \: ............(ii)$

$\rm\large \green{TO \: \: \: FIND} \pink{ \rightarrow}$

$\sf \: value \: \: of \: x \: and \: y$

$\green{ \large \rm \: SOLUTION} \pink{ \rightarrow}$

$\sf \: From \: eq \: . (i) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \: 5x - 4y + 8 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \green{ \rightarrow} \sf \: 5x = 4y- 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: \: \green{ \rightarrow} \sf \: x = \frac{4y - 8}{5} \: \: \: \: \: \: \: \: \: \: \: ...(iii)$

$\sf \: Put \: the \: value \: of \: x \: in \: eq. (ii) \: \\ \sf \: we\: get.. \\ \sf7x + 6y - 9 = 0 \\ \\ \green{ \rightarrow} \sf \: 7 \bigg( \frac{4y - 8}{5} \bigg) + 6y = 9 \\ \\ \sf \: \green{ \rightarrow} \frac{7(4y - 8)}{5} + 6y = 9 \: \: \: \: \\ \\ \sf \: \green{ \rightarrow} \frac{28y - 56 + 5(6y)}{5} = 9 \\ \\ \sf \: \green{ \rightarrow} \frac{28y - 56 + 30y}{5} = 9 \: \: \\ \\ \sf \: \green{ \rightarrow} \frac{58y - 56}{5} = 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\green{ \rightarrow}58y - 56 = 9 \times 5 \: \: \: \: \: \\ \\ \sf \: \green{ \rightarrow} \: 58y = 45 + 56 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: \green{ \rightarrow} \: 58y \: = 101 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: \green{ \rightarrow}y= \frac{101}{58} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf \: Put \: the \: value \: of \: y \: i n \: eq. (iii) \\ \sf \: we \: get.. ....$

$\displaystyle \: \sf \: x = \frac{4y - 8}{5} \: \: \: \: \: \: \: \: \: \: \\ \\ \green{ \rightarrow} \sf \: x = \frac{4 \big( \frac{101}{58}) - 8}{5} \\ \\ \sf \: \green{ \rightarrow}x = \frac{ \frac{404}{58} - 8}{5} \: \: \: \: \: \: \: \: \\ \\ \sf\green{ \rightarrow}x = \frac{ \frac{404 - 464}{58} }{5} \\ \\ \sf \: \green{ \rightarrow}x = \frac{ \frac{ - 60}{58} }{5} \\ \\ \sf \: \green{ \rightarrow} \: x = - \frac{6}{29}$

$\sf \: Hence \: \green{ \boxed{x = - \frac{6}{29}}} \: , \green{ \boxed{ y = \frac{101}{58} }}$