Chapter 11: Q. 346 (page 1160)

Solve the nonlinear system of equations using substitution:
$\{\begin{cases} x^{2} + y^{2} = 8 \\ y = - x - 4 \end{cases}$

Short Answer

Expert verified

The type of graph for the given equations are circle and line.

Step by step solution

Step 1. Given Information

Given that the equation is $\{\begin{cases} x^{2} + y^{2} = 8 \\ y = - x - 4 \end{cases} .$

Step 2. Form of the equation

In the first equation, there is same coefficient of $x^{2} and y^{2} .$ When a linear equation have two variable and it is line. The solution of $x^{2} + y^{2} = 8$ is circle and $y = - x - 4$ is line. On comparing the equation with the standard form,

${(x - 0)}^{2} + {(y - 0)}^{2} = 2 \sqrt{2} h = 0, k = 0 y = - x - 4 m = - 1, b = - 4 (h, k) = (0, 0)$

The standard form of $x^{2} + y^{2} = 8 is {(x - 0)}^{2} + {(y - 0)}^{2} = 2 \sqrt{2} and y = - x - 4 is y = - x - 4 .$

Step 3. Graph

On drawing the graph,

Step 4. Solution

The circle and line intersected at (-2,2) . On verifying the point in the equation by substitution,

$x^{2} + y^{2} = 8 {(- 2)}^{2} + {(- 2)}^{2} = 8 8 = 8 y = - 2 x - 1 - 2 = - 2 (- 2) - 4 - 2 = - 2$

It satisfies both the equation. Hence, the solution is (-2,2).

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Solve the nonlinear system of equations using substitution:
$\{\begin{cases} x^{2} + y^{2} = 8 \\ y = - x - 4 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form of the equation

Step 3. Graph

Step 4. Solution

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Solve the nonlinear system of equations using substitution:x2+y2=8y=-x-4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form of the equation

Step 3. Graph

Step 4. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Calculus

Probability and Statistics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve the nonlinear system of equations using substitution:
$\{\begin{cases} x^{2} + y^{2} = 8 \\ y = - x - 4 \end{cases}$