Chapter 11: Q. 204 (page 1147)

In the following exercises, solve the system of equations by using substitution.
$\{\begin{cases} 4 x^{2} + y^{2} = 4 \\ y = 4 \end{cases}$

Short Answer

Expert verified

The system has no real solution.

Step by step solution

Step 1. Given Information

The given system of equations is $\{\begin{cases} 4 x^{2} + y^{2} = 4 \\ y = 4 \end{cases}$

Step 2. Substitution

Substitute $y = 4$ into $4 x^{2} + y^{2} = 4$ and simplify.

$\begin{array}{rcl} 4 x^{2} + {(4)}^{2} & = & 4 \\ 4 x^{2} + 16 & = & 4 \\ 4 x^{2} + 12 & = & 0 \end{array}$

As $0^{2} - 4 (4) (12) < 0$ , there are no real roots of the system.
As no real value ofxexists, the system has no solution.

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In the following exercises, solve the system of equations by using substitution.
$\{\begin{cases} 4 x^{2} + y^{2} = 4 \\ y = 4 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Substitution

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In the following exercises, solve the system of equations by using substitution.4x2+y2=4y=4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Substitution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve the system of equations by using substitution.
$\{\begin{cases} 4 x^{2} + y^{2} = 4 \\ y = 4 \end{cases}$