Chapter 6.6, Problem 56STP

To determine

To graph: the equations

  $\begin{array}{l}3x+2y=8\\ -4x+6y=11\end{array}$

Explanation of Solution

Given information:

The equation

  $\begin{array}{l}3x+2y=8\\ -4x+6y=11\end{array}$

Graph:

Consider the equations:-

  $\begin{array}{l}3x+2y=8\\ -4x+6y=11\end{array}$

Re − writing the equation in slope- intercept form-

  $\begin{array}{l}3x+2y=8\\ 2y=8-3x\\ \frac{2y}{2}=\frac{8}{2}-\frac{3x}{2}\\ y=4-\frac{3}{2}x\text{ (i)}\end{array}$

  $\begin{array}{l}-4x+6y=11\\ 6y=11+4x\\ \frac{6y}{6}=\frac{11}{6}+\frac{4x}{6}\\ y=\frac{11}{6}+\frac{2}{3}x\text{ (ii)}\end{array}$

Equations are :-

  $\begin{array}{l}y=4-\frac{3}{2}x\\ y=\frac{11}{6}+\frac{2}{3}x\end{array}$

  

Figure 1.

Interpretation:

The graphs of the lines appear to intersect at $(1,2.5)$ . The equation $y=4-\frac{3}{2}x$ (red line) crosses x -axis at point $(2.667,0)$ and y -axis at $(0,4)$ whereas the equation $y=\frac{11}{6}+\frac{2}{3}x$ (blue line) crosses x -axis at $(-2.75,0)$ and y -axis at $(0,1.88)$ .