Question

determine the value of a if the system of linear equation 3x+2y-4=0 and ax-y-3=0 will represent interacting line
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Answer 1

Correct Question:

Determine the value of a if the system of linear equation 3x+2y-4=0 and ax-y-3=0 will represent intersecting lines.

Answer:

(1/x-3/2)

a ≠ -3/2

Step-by-step explanation:

Given a pair of linear equations such that,

3x + 2y - 4 = 0 .......(1)

ax - y - 3 = 0 .......(2)

Now, we know that,

A linear equation represents a line.

Also, it's said that, both of these lines intersect each other.

Now, Let's assume that the point of intersection is (x,y).

Therefore, we will have,

(x,y) satisfying both the equations.

Now, from eqn (2), we get,

=> y = ax -3

Now, substituting this value in (1), we get,

=> 3x + 2(ax-3) - 4 = 0

=> 3x + 2ax - 6 + 4 = 0

=> 3x + 2ax - 2 = 0

=> 3x + 2ax = 2

=> 2ax = 2-3x

=> a = (2-3x)/2x

=> a = 1/x - 3/2

Hence, the required value of a is (1/x - 3/2).

Also, it's clear that,

There will be only one solution for this pair of linear equations as they are intersecting.

Therefore, we have,

• a1/a2 ≠ b1/b2

Therefore, we will get,

=> 3/a ≠ 2/-1

=> 3/a ≠ -2

=> a ≠ -3/2

Hence, we have, a ≠ -3/2.