Question

Pair of linear equations x+2y=5, x-8y=15 are
1.Parallel


2.Intersecting


3.Coincident


4.None of these​

Answer 1

Answer:

answer of this question is 2 intersecting

Answer 2

Concept

Two lines are parallel if they do not have any solution in common. They are coincidental if they have infinitely many solutions in common. Finally, they are intersecting if they have only 1 point in common.

Given

a pair of linear equations

x + 2y = 5

and x - 8y = 15

Find

we need to find if the equations are parallel, intersecting, coincidental or none of these.

Solution

We have

x + 2y = 5

and x - 8y = 15

here, a1 = 1, a2 = 1

b1 = 2, b2 = -8

c1 = 5, c2 = 15

Thus, a1/a2 = 1

b1/b2 = -1/4

c1/c2 = 1/3

These are not equal to each other so the lines are neither parallel nor coincidental.

Subtracting both the equations, we get

x - 8y -x - 2y = 15 - 5

-10y = 10

y = -1

x = 7

Thus, the lines will intersect each other at point (-1,7). Hence option 2 is correct.

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