Question

Given the system of linear equations provide the following information for each system

Answer 1

We are given the following system of equations:

`\begin{gathered} y=(3)/(4)x+2,(1) \\ -6x+8y=16,(2) \end{gathered}`

We will solve for "y" in equation (2), first by adding "6x" to both sides:

`8y=6x+16`

Now we will divide both sides by 8:

`y=(6x)/(8)+(16)/(8)`

Simplifying we get:

`y=(3x)/(4)+2`

The new equivalent system is:

`\begin{gathered} y=(3)/(4)x+2,(1) \\ y=(3)/(4)x+2,(2) \end{gathered}`

This system of the form:

`\begin{gathered} y=m_1x+b_1 \\ y=m_2x+b_2 \end{gathered}`

Where "m" represents the slopes of each equation and "b" represents the y-intercepts. From the given system we have:

`\begin{gathered} m_1=(3)/(4) \\ m_2=(3)/(4) \\ b_1=2 \\ b_2=2 \end{gathered}`

Since the slopes are the same this means that the system has infinite solutions.