f4Equations of Straight Lines

(1) If the straight lines L1:2x+y+1=2 and L2: x-2y+8=0 intersect at point Q, find
(a) the coordinates of Q.
2x+y+1=2 [ would it be 2x+y+1=0 ? ]
y=1-2x
sub into x-2y+8=0
x-2(1-2x)+8=0
x-2+4x+8=0
5x+6=0
x=-6/5
y=1-2(-6/5)=1+12/5=17/5
Q is (-6/5,17/5)

if 2x+y+1=0
y=-1-2x
sub into x-2y+8=0
x-2(-1-2x)+8=0
x+2+4x+8=0
5x=-10
x=-2
y=-1-2x=-1-2(-2)=-1+4=3
Q is (-2,3)
(b) the equation of the straight line L passing through Q and parallel to the y-axis

A straight line parallel to y-axis would be y=k; [ slope=0 ]
therefore, y=17/5 or y=3 is the required line. it depends on Q is (-6/5,17/5) or Q is (-2,3).

(2) It is given that R is the intersection of the two straight lines L1:4x-3y-15=0
and L2: 3x-7y+3=0
(a) find the coordinates of R.

4x-3y-15=0
4x=3y+15
x=(3y+15)/4
sub into 3x-7y+3=0
3[(3y+15)/4]-7y+3=0
3(3y+15)-28y+12=0
9y+45-28y+12=0
-19y+57=0
y=3
x=(3y+15)/4=6
R is (6,3)
(b) If L is the the straight lines passing through R and the origin, find the equation of L

(y-0)/(x-0)=(3-0)/(6-0)
y/x=1/2
2y=x
2y-x=0