Question

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

Answer 1

Complete Question

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

`x - 3y = -10 \ \ \ and \ \ \ 4x +3y = 20`

Answer:

This system of linear equations has one solution which is (x, y) = (2,4 )

Explanation:

The first step is to add that two linear equations

`x - 3y = -10\cdots (i) \\ 4x + 3y = 20\cdots (ii)\\------\\ 5x \ \ \ \ \ \ \ = 10`

=>
`x = 2`

substituting this into equation i we have

`2 - 3y = -10`

=>
`y = 4`

Hence this system of linear equations has one solution which is (x, y) = (2,4 )