Question

Find the point of intersection (if any) of the following pairs of lines: a) x – 2y +1=0 2x + 3y – 7 = 0 b) x-2y+11=0 -x+2y-13 = 0

Answer 1

Answer:

a) (11/7, 9/7)

b) There's no point of intersection

Step-by-step explanation:

a) x - 2y + 1 = 0

2x + 3y - 7 = 0

To find the point of intersection, we need to solve the system of equations  and the result will be the point of intersection (x,y)

$x-2y+1=0\\x= 2y-1$

Now we substitute x in the second equation:

$2x+3y-7=0\\2(2y-1)+3y-7=0\\4y-2+3y-7=0\\7y-9=0\\y=9/7$

Now we substitute y in our first equation.

$x-2y+1=0\\x-2(9/7)+1=0\\x-18/7+1=0\\x=18/7-1\\x=11/7$.

The point of intersection is (11/7, 9/7)

b) x -2y +11 =0

-x + 2y - 13 =0

We are going to follow the same procedure:

$x-2y+11=0\\x=2y-11$

$-(2y-11)+2y-13=0\\-2y+11+2y-13=0\\0y=2\\0=2$

Since this system of equations doesn't have a solution, the system has no point of intersection.