Question

Solve the following system of linear equations by addition. Indicate whether the given system of linear equations has one solution, hasno solution, or has an infinite number of solutions. If the system has one solution, find the solution.| 0.6x +0.2y = 4.6{ =

Answer 1

Answer: ( -8, 47 )

Given:

`\begin{cases}0.6x+0.2y=4.6 \\ 1.5x+0.3y=2.1\end{cases}`

First, let us multiply equation 1 by 3, and equation 2 by -2. We will now get:

`\begin{cases}1.8x+0.6y=13.8 \\ -3x-0.6y=-4.2\end{cases}`

Add the two equations and we will get:

`-1.2x=9.6`

*Divide both sides by -1.2

`x=(9.6)/(-1.2)=-8`

Now, going back to the equations, we can choose any of the two to find the value of y.

Using equation 1:

`0.6x+0.2y=4.6`
`0.6(-8)+0.2y=4.6`
`0.2y=4.6+4.8`
`0.2y=9.4`

*Divide both sides by 0.2

`y=(9.4)/(0.2)=47`

Therefore, the solution to this system of equation is ( -8, 47 )