Answer:
[tex]y=2x-3[/tex]
Step-by-step explanation:
1. Using the point of intersections, we use the substitution method to find the coordinates of the line parallel to [tex]2x-y-9=0[/tex]
[tex]5x+y+4=0[/tex]
[tex]y= -4-5x[/tex]
substituting the value of y in [tex]2x+3y=1[/tex]:
[tex]2x +3(-4-5x)=1\\\\2x-12-15x-1=0\\-13x=13x\\x= \frac{13}{-13}= -1[/tex]
substituting x=-1 in y= -4-5x:
[tex]y= 1[/tex] (upon solving, you should get this)
[tex](x,y)= (-1,1)[/tex]
2. Using y=mx+c and making y the subject of the formula 2x-y-9=0 and using the coordinate we found earlier, we will find the equation of the parallel line. (We make y the subject of the formula to find the gradient)
[tex]2x-y-9=0\\2x-9=y\\y= 2x-9[/tex]
[tex]y= mx+c\\[/tex]
-1= 2 x 1 +c
-3=c