Question

How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x-2y= 10 and -6x +4y= -20?

Answer 1

See the explanation.

Explanation:

`3x-2y=10`
`-6x+4y=-20 | :(-2)`

`3x-2y=10`
`3x-2y=10`

So, we get system of two equal equations and because of that, it has many solutions.

Let's pick one unknown as a parameter: `x=K`, then:

`3K-2y=10 => 2y=3K-10 => y=(3K-10)/2=3/2K-5`

Every pair `(K,3/2K-5)` where `K in R` is solution of given system.