smart Mathematicians i need your help. Pls clearly explain your workings?

Question

1)
Find the value of N if the straight line Nx - y = 9 is parallel to the line y = 1/2x + 2

2)
I need points in other to find straight lines determined by y = 2x -3 and x + 6 = 2y. Also find the
coordinates of the intersection.

Answer 1

1) as two lines are parallel therefore we know that
a1x+b1y+c1=0
a2x+b2y+c2=0
if two are parallel
then a1=a2
b1=b2
therefore
Nx-y-9=0
1/2x-y+2=0
N=1/2

2)
u can find points 4 two equation by keeping x or y =0
so for 1st eq.
x=0 then y=-3 therefore (0,-3) lies in first equation there is one more point if we keep y=0 then x=3/2 (3/2,0)
for 2nd eq.
keep x=0 and then y=3 (0,3) and keep y=0 then x=-6 (-6,0)
point of intersection is
solve both simultaneously
2(2x-y-3=0)
4x-2y-6=0
2y-x-6=0
u will get y=5 and x=4
(4,5)

Answer 2

1) First line is y=Nx-9. Two parallel lines have the same slope. The slope is the factor multiplying x, therefore N=1/2.

Replace y with 2x-3 in the second equation and solve for x.

Answer 3

1 ) .5
Parallel lines have the same slope ( the coeffient before x)

2 ) ( 4 , 5 )
The intersection is where the two equations are both true.
2 * ( 2x - 3 ) = x + 6
4x - 6 = x + 6
4x = x + 12
3x = 12
x = 4
So now you know the x value. Plug in the 4 in one of the equations to find the y value.
x + 6 = 2y
4 +6 = 2y
10 = 2y
5 = y

Answer 4

Some hints:
Problem 1. Write both equations in the form
y = mx + b. Two lines are parallel if they have
the same ______.

Problem 2. The first sentence makes no sense.
To find the point of intersection, we must
solve the system
2x -y = 3
x - 2y = -6
You can carry on from here!

Answer 5

parallel to the line 1/2x+2
slope=1/2
N=1/2

2.y=2x-3
4y=2x+12 subtracting
3y=15 and y=5
sub x=4
point of intersection ={4,5}