Question

solve by substitution method 6x-7y+25=0,5x-9y+1=0

Answer 1

Given Equation is 6x - 7y + 25 = 0  ----- (1)

6x = 7y - 25

$x = \frac{7y - 25}{6}$   ------ (2)

Given Equation is 5x - 9y + 1 = 0   ----- (3)

Substitute (2) in (3), we get.

$5( \frac{7y - 25}{6} ) - 9y + 1 = 0$

$5( \frac{7y - 25}{6}) - 9y = -1$

5(7y - 25) - 54y = -6

35y - 125 - 54y = -6

-19y - 125 = -6

-19y = 119

y = -119/19.


Substitute y = -119/19 in (1), we get

6x - 7y + 25 = 0

6x - 7(-119/19) + 25 = 0

6x + 833/19 + 25 = 0

$6x + \frac{19 * 25 + 833}{19} = 0$

$6x + \frac{1308}{19} = 0$

$6x = - \frac{1308}{19}$

$x = - \frac{1308}{19 * 6}$

$x = - \frac{1308}{114}$

$x = - \frac{218}{19}$


Therefore x = -218/19 and y = -119/19.


Hope this helps!