Question

Solve the following system of linear equations by graphing:46x + y = 4383+ + 2y = -1

Answer 1

Given the equation;

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

The slope-intercept form is given as;

`y=mx+c`

Rewriting the equations in slope-intercept form gives;

`\begin{gathered} -(4)/(3)x+y=4 \\ y=(4)/(3)x+4\ldots.\ldots..\ldots\ldots...\ldots\text{equation 1} \end{gathered}`

Also;

`\begin{gathered} -(8)/(3)x+2y=-1 \\ 2y=(8)/(3)x-1 \\ y=(4)/(3)x-(1)/(2)\ldots\ldots...\ldots\ldots\ldots\text{equation 2} \end{gathered}`

Equation 1 and equation 2 have an equal solution. Thus, the lines are parallel to each other. In otherwords, the lines cannot intersect.

The graph is;

The equations in slope-interceot form are;

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