Chapter 3.2, Problem 27WE

To determine

To graph: The given pair of equations, then to find their point of intersection and to verify by substitution that the coordinates satisfy both equations.

Answer to Problem 27WE

The graphs intersect at the point $(5,-2)$ and these coordinates satisfy both equations.

Explanation of Solution

Given information: Given pair of equations is: $\begin{array}{l}2x+5y=0\\ 2x+y=8\end{array}$

Graph:

First equation is: $2x+5y=0$

  $\begin{array}{lll}x\hfill & 0\hfill & -2.5\hfill \\ y\hfill & 0\hfill & 1\hfill \end{array}$

So the graph of $2x+5y=0$ passes through $(0,0)and(-2.5,1)$ .

Second equation is: $2x+y=8$

  $\begin{array}{lll}x\hfill & 2\hfill & 4\hfill \\ y\hfill & 4\hfill & 0\hfill \end{array}$

So the graph of $2x+y=8$ passes through $(0,8)and(4,0)$ .

Thus, the graphs are:

  

Interpretation:

The graphs intersect at the point $(5,-2)$ .

Verification:

Putting $x=5,y=-2$ in $2x+5y=0$ ,

  $\begin{array}{l}2(5)+5(-2)=0\\ \Rightarrow 10-10=0\\ \Rightarrow 0=0\end{array}$

which is true.

Putting $x=5,y=-2$ in $2x+y=8$ ,

  $\begin{array}{l}2(5)-2=8\\ \Rightarrow 8=8\end{array}$

which is true.

Thus, the coordinates satisfy both equations.