Question

If the three lines y= x+4 , 2y +x=2 and y= ax+8 are concurrent, find the value of a.​

Answer 1

a=3

Explanation:

Three or more lines in a plane are said to be concurrent if they intersect at a single point.

First find the point of intersection of lines y=x+4 and 2y+x=2. Substitute y=x+4 into the second equation:

2(x+4)+x=2

2x+8+x=2

2x+x=2-8

3x=-6

x=-2

Then

y=-2+4=2

So, the point of intersection is (-2,2). The coordinates of this point must satisfy the equation of the third line, thus

2=a·(-2)+8

2=-2a+8

2a=8-2

2a=6

a=3