Question

Find the y-intercept of the line with slope –5/3 that passes through the
point of intersection of the lines:
2014x + 2015y = 2016
2019x + 2018y = 2017

Answer 1

first of all we have to find out intersection point of the lines :
$2014x + 2015y = 2016\\2019x+2018y=2017$

add both the given equations ,
(2014 + 2019)x + (2015 + 2018)y = 2016 + 2017
4033x + 4033y = 4033
x + y = 1 , y = (1 - x) -----(1)

put equation (1) in 2014x + 2015y = 2016
2014x + 2015 - 2015x = 2016
-x = 1 => x = -1 so, y = 2

hence, intersection point of given lines is (-1,2)
so, equation of line is given by $\bf{y-y_1=m(x-x_1)}$
here m = slope of line = -5/3
and (x1, y1) = (-1,2)
so, (y - 2) = -5/3(x + 1)
=> 3(y - 2) + 5(x + 1) = 0
=> 3y - 6 + 5x + 5 = 0
=> 5x + 3y - 1 = 0
=> 3y = 1 - 5x
=> y = 1/5 + (-5/3)x
hence, y - intercept of line is 1/5