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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 201 (page 1147)

In the following exercises, solve the system of equations by using substitution
$\{\begin{matrix} 9 x^{2} + y^{2} = 9 \\ y = 3 x + 3 \end{matrix}$

Short Answer

Expert verified

The solutions of the system are $(0, 3), (- 1, 0)$ .

Step by step solution

01

Step 1. Given information

The given system of equations is $\{\begin{matrix} 9 x^{2} + y^{2} = 9 \\ y = 3 x + 3 \end{matrix}$

02

Step 2. Substitution

Substitute $y = 3 x + 3$ into $9 x^{2} + y^{2} = 9$ and solve for x.

$\begin{array}{rcl} 9 x^{2} + {(3 x + 3)}^{2} & = & 9 9 x^{2} + 9 x^{2} + 9 + 18 x = 9 \\ 18 x^{2} + 18 & = & 0 \\ 18 x (x + 1) & = & 0 \end{array}$

So, the values ofxare $0, - 1$ .

03

Step 3. Solve for y

Substitute $x = 0$ into $y = 3 x + 3$ and solve for y.

$\begin{array}{rcl} y & = & 3 脳 0 + 3 \\ = & 3 \end{array}$

Substitute $x = - 1$ into $y = 3 x + 3$ and solve for y.

$\begin{array}{rcl} y & = & 3 脳 - 1 + 3 \\ = & 0 \end{array}$

So, the solutions of the system are $(0, 3), (- 1, 0)$

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