Question

the path traced by two maruti cars are given by the equation x+2y-4=0 and 2x+4y-12=0. find out wheater their paths will cross or not​

Answer 1

Answer:

Not

Step-by-step explanation:

If their paths are crossed, there must a defined place where these two paths meet.

Mathematically, if two lines(paths) meet, they meet at a defined point(place) which lies on both the lines.

If that point exists, they cross each other.

Let that point exists and that is (a, b). For (x, y) = (a, b)

Eqⁿ are a + 2b - 4 = 0, ...(1)

and, 2a + 4b - 12 = 0 ... (2)

Subtract (1) from (2), we get

a + 2b - 8 = 0

Notice a + 2b - 4 = 0 and a + 2b - 8 = 0

→ a + 2b = 4 and a + 2b = 8

As LHS is same in both but RHS is different, 'a' and 'b' are not defined(same linear eqⁿ can't give two different values).

This means, there is no such point(a, b) that satisfies x + 2y - 4 = 0 and 2x + 4y - 12 = 0.

Hence, these lines never meet.

Answer 2

Given :-

x + 2y - 4 = 0

2x + 4y - 12 = 0

To Find :-

Whether they will meet or not

Solution :-

Let

x + 2y - 4 = 0 (Eq 1)

2x + 4y - 12 = 0 (Eq 2)

The second equation could be divided by 2

2x + 4y - 12/2 = 0/2

x + 2y - 12 = 0 (Eq 3)

Now

Eq 1 and Eq 3 must be equal to say that they will cross

Eq 1 -

x + 2y - 4 = 0

x + 2y = 0 + 4

x + 2y = 4

Eq 3 -

x + 2y - 12 = 0

x + 2y = 0 + 12

x + 2y = 12

Since

LHS are equal but RHS aren't equal. So, they will not cross each other

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