Exercise 96 Page 617

To solve the system of equations by graphing, we will draw both the exponential function and the linear function on the same coordinate grid.

Graphing Exponential Function

We want to draw a graph of the given exponential function. To draw the graph, we will start by making a table of values.

$x$	$2^x$	$y=2^x$
$\text{-}2$	$2^{\text{-}2}$	$0.25$
$\text{-}1$	$2^{\text{-}1}$	$0.5$
$0$	$2^0$	$1$
$1$	$2^1$	$2$
$2$	$2^2$	$4$
$3$	$2^3$	$8$

The ordered pairs $(\text{-}2,0.25),$ $(\text{-}1,0.5),$ $(0,1),$ $(1,2),$ $(2,4),$ and $(3,8)$ all lie on the graph of the function. Now, we will plot and connect them with a smooth curve.

Graphing Linear Function

Let's now graph the linear function on the same coordinate plane. For a linear equation written in slope-intercept form, we can identify its slope $m$ and $y\text{-}$intercept $b.$ The slope of the line is $\text{-}1$ and the $y\text{-}$intercept is $5.$

Finding the Solutions

Finally, let's try to identify the coordinates of the points of intersection of the parabola and the line.

It looks like the point of intersection occurs at $(1.7,3.3).$

Checking the Answer

To check our answer, we will substitute the value of the point of intersection in both equations of the system. If it produces true statements, our solution is correct. Equation (II) produced a true statement. In Equation (I), the answer is an approximation. This is because we could not state an exact answer just by looking at the graph, but we obtained a decent approximation. Therefore, we can say that $(1.7,3.3)$ is an approximated answer.