Chapter 11: Q. 23 (page 772)

graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} - 4 \\ y = 6 x - 13 \end{cases}$

Short Answer

Expert verified

the point of intersection is $(3, 5)$ .

Step by step solution

Step 1. Given

$\{\begin{cases} y = x^{2} - 4 \\ y = 6 x - 13 \end{cases}$

Step 2. Graphing each equation

$y = x^{2} - 4$

$y = 6 x - 13$

Step 3. Calculation of intersection point

$C o n s i d e r, y = x^{2} - 4 . . . . . (1) y = 6 x - 13 . . . . . (2) N o w s u b s t i t u t i n g t h e v a l u e o f y f r o m e q . 1 i n t o e q . 2 w e g e t x^{2} - 4 = 6 x - 13 x^{2} - 6 x + 9 = 0 {(x - 3)}^{2} = 0 x = 3 N o w s u b s t i t u t i n g v a l u e o f x i n e q . 1 w e g e t y = {(3)}^{2} - 4 y = 5$

Step 4. Check the solution

$S u b s t i t u t e t h e o b t a i n e d v a l u e s o f x a n d y i n b o t h t h e e q u a t i o n s y = 6 x - 13 5 = 6 (3) - 13 5 = 5 a l s o y = x^{2} - 4 5 = {(3)}^{2} - 4 5 = 5 h o l d s t r u e .$

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graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} - 4 \\ y = 6 x - 13 \end{cases}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Graphing each equation

Step 3. Calculation of intersection point

Step 4. Check the solution

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graph each equation of the system. Then solve the system to find the points of intersection.y=x2-4y=6x-13

Short Answer

Step by step solution

Step 1. Given

Step 2. Graphing each equation

Step 3. Calculation of intersection point

Step 4. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Calculus

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} - 4 \\ y = 6 x - 13 \end{cases}$