Question

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 0.3x − 0.2y = 0.4 −0.2x + 0.5y = 0.1

Answer 1

`x=2` and
`y=1`

Explanation:

We have two linear equations

`0.3x-0.2y=0.4`

`-0.2x+0.5y=0.1`

Using the methond of elimination of variables, we will mutiply the first equation by 0.2 and the second one by 0.3 to have the same value of the varible x.

`(0.3x-0.2y=0.4)0.2`

`(-0.2x+0.5y=0.1)0.3`

Then

`0.06x-0.04y=0.08`

`-0.06x+0.15y=0.03`

Adding both equation we will eliminate the varible x

`0.11y=0.11`

Then the value of y is
`y=1`

Now with the value of y we can find x, using the value of y in the first equation we have:

`0.3x-0.2(1)=0.4`

`0.3x-0.2=0.4`

`0.3x=0.4+0.2`

`0.3x=0.6`

`x=(0.6)/(0.3)`

`x=2`