Chapter 11: Q. 21 (page 796)

In Problems $21$ and $22$ , solve each system of equations.
$\{\begin{array}{r} 3 x^{2} + y^{2} = 12 \\ y^{2} = 9 x \end{array}$

Short Answer

Expert verified

Solution of the system of equations is $(1, \pm 3)$

Step by step solution

Step 1. Given information

A system of equations is given as

$\{\begin{array}{r} 3 x^{2} + y^{2} = 12 \\ y^{2} = 9 x \end{array}$

Step 2. Solving for x

We will use substitution method,

Divide the equation $3 x^{2} + 9 x = 12$ by $3$ ,

$x^{2} + 3 x - 4 = 0$

Now, solve as quadratic equation,

$\begin{array}{r} x^{2} - x + 4 x - 4 = 0 \\ x (x - 1) + 4 (x - 1) = 0 \\ (x + 4) (x - 1) = 0 \end{array}$

Now xhas two values but according to the system of equations xcannot be negative.

Therefore xmust be one.

Step 3. Solve for y

Now substitute the values of x,

$y^{2} = 9 (1) y = \pm 3$

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In Problems $21$ and $22$ , solve each system of equations.
$\{\begin{array}{r} 3 x^{2} + y^{2} = 12 \\ y^{2} = 9 x \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for x

Step 3. Solve for y

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In Problems 21and 22, solve each system of equations. 3x2+y2=12y2=9x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for x

Step 3. Solve for y

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

Pure Maths

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems $21$ and $22$ , solve each system of equations.
$\{\begin{array}{r} 3 x^{2} + y^{2} = 12 \\ y^{2} = 9 x \end{array}$