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Expert-verified Found in: Page 772 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.$y=\sqrt{4-{x}^{2}};\phantom{\rule{0ex}{0ex}}y=2x+4$

he graph of the system of equations $y=\sqrt{4-{x}^{2}};y=2x+4$ is:

The points of intersection are $\left(-\frac{6}{5},\frac{8}{5}\right),\left(-2,0\right)$

See the step by step solution

## Step 1. Given

The system of non-linear equation:

$y=\sqrt{4-{x}^{2}};\phantom{\rule{0ex}{0ex}}y=2x+4$

To graph the equation and to find the point of intersection.

## Step 2. Graph the equations

Graph the equations in the same plane. ## Step 3. To find the point of intersection.

Equate both the equations,

$\sqrt{4-{x}^{2}}=2x+4$

Squaring on both sides, we get,

$4-{x}^{2}={\left(2x+4\right)}^{2}\phantom{\rule{0ex}{0ex}}4-{x}^{2}=4{x}^{2}+16x+16\phantom{\rule{0ex}{0ex}}5{x}^{2}+16x+12=0$

## Step 4. Solve the equations

$5{x}^{2}+16x+12=0\phantom{\rule{0ex}{0ex}}\left(5x+6\right)\left(x+2\right)=0\phantom{\rule{0ex}{0ex}}x=-\frac{6}{5},-2$

The value of $x$ is $-\frac{6}{5},-2$

## Step 5. Find y

When

$x=-\frac{6}{5},\phantom{\rule{0ex}{0ex}}y=2x+4\phantom{\rule{0ex}{0ex}}=2\left(-\frac{6}{5}\right)+4\phantom{\rule{0ex}{0ex}}=-\frac{12}{5}+4\phantom{\rule{0ex}{0ex}}=\frac{8}{5}$

When $x=-2,$

$y=2x+4\phantom{\rule{0ex}{0ex}}=2\left(-2\right)+4\phantom{\rule{0ex}{0ex}}=0$

The point of intersections are $\left(-\frac{6}{5},\frac{8}{5}\right),\left(-2,0\right)$ ### Want to see more solutions like these? 