Chapter 11: Q. 202 (page 1147)

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

Short Answer

Expert verified

The solution of the system is $(0, 3), (- 0.6, 2.4)$ .

Step by step solution

Step 1. Given information

The given system is

$\{\begin{cases} 9 x^{2} + y^{2} = 9 \\ y = x + 3 \end{cases}$

Step 2. Substitution

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

$\begin{array}{rcl} 9 x^{2} + {(x + 3)}^{2} & = & 9 9 x^{2} + x^{2} + 9 + 6 x = 9 \\ 10 x^{2} + 6 x & = & 0 \\ 2 x (5 x + 3) & = & 0 \end{array}$

So,localid="1645720229483" $x = 0, - 0.6$ .

Step 3. Solve for y

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

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

Substitute $x = - 0.6$ into $y = x + 3$ and solve for y.

$\begin{array}{rcl} y & = & - 0.6 \\ = & 2.4 \end{array}$

So, the solution of the system is $(0, 3), (- 0.6, 2.4)$ .

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitution

Step 3. Solve for y

One App. One Place for Learning.

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In the following exercises, solve the system of equations by using substitution9x2+y2=9y=x+3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitution

Step 3. Solve for y

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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