Question

Consider the equation 5x-2y=3. If possible, find a second linear equation to create a system of equations that has: Exactly one solution Exactly two solutions No solutions Infinitely many solutions

Answer 1

Answer with explanation:

1.⇒ The given equation is

5x-2y=3

For one solution ,you should write linear equation in such a way

ax+by=c, such that

`(5)/(a)\\eq (-2)/(b)\\eq (3)/(c)`

So, the linear equation will be

→3x+4y=8

You can write many more by yourself.

2.⇒Exactly two solutions

The two lines intersect at only one point.So,there are no such lines which has two point of Intersection.

3.⇒No solutions

It means the two lines will never intersect.

For no solution ,you should write equation of line in such a way

ax+by=c, such that

`(5)/(a)=(-2)/(b)\\eq (3)/(c)`

So, the linear equation will be

→10x -4y=15

You can write many more by yourself.

4.⇒Infinitely many solutions

For Infinite number of solution ,you should write linear equation in such a way

ax+by=c, such that

`(5)/(a)=(-2)/(b)=(3)/(c)`

→10x-4y=6

Answer 2

a) One solution: 5x +2y = 0 . . . . (any line with a different slope)

b) Two solutions: not possible

c) No solutions: 5x -2y = 0 . . . . (any different line with the same slope)

d) Infinitely many solutions: 10x -4y = 6 . . . . (any other equation for the same line)