Chapter 11: Q. 5 (page 772)

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} + 1 \\ y = x + 1 \end{cases}$

Short Answer

Expert verified

Solutions of system of equations $\{\begin{cases} y = x^{2} + 1 \\ y = x + 1 \end{cases}$ are $(0, 1) & (1, 2)$ and the graph is

Step by step solution

Step 1. Given data

The given system of equations is

$\begin{array}{l} y = x^{2} + 1 \dots (i) \\ y = x + 1 \dots (i i) \end{array}$

Step 2. Graph of the system of equations

Plot the graph of $y = x^{2} + 1 & y = x + 1$ on same cartesian plane

Step 3. Solution of system

subtract equation ii from equation i

$y - y = (x^{2} + 1) - (x + 1) 0 = x^{2} - x x (x - 1) = 0$

By zero product property

$x = 0$

$x - 1 = 0 x = 1$

So solutions are $(0, 1) & (1, 2)$

Step 4. Solution of system

Substitute $x = 0$ in equation ii

role="math" localid="1646867196591" $y = x + 1 y = 0 + 1 y = 1$

Substitute $x = 1$ in equation ii

role="math" $y = x + 1 y = 1 + 1 y = 2$

So solutions of the system arerole="math" localid="1646867593062" $(0, 1) & (1, 2)$

Step 5. Verification

Substitute $x = 0 & y = 1$ in the system

$\{\begin{cases} 1 = 0^{2} + 1 \\ 1 = 0 + 1 \end{cases} \to \{\begin{cases} 1 = 1 \\ 1 = 1 \end{cases}$

Substitute $x = 1 & y = 2$ in system

$\{\begin{cases} 2 = 1^{2} + 1 \\ 2 = 1 + 1 \end{cases} \to \{\begin{cases} 2 = 2 \\ 2 = 2 \end{cases}$

The system of equations is satisfied by both solutions

so solutions $(0, 1) & (1, 2)$ are correct

Step 6. Point of intersection

Locate the $(0, 1) & (1, 2)$ for point of interception in the graph of a system of equations

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Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} + 1 \\ y = x + 1 \end{cases}$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Graph of the system of equations

Step 3. Solution of system

Step 4. Solution of system

Step 5. Verification

Step 6. Point of intersection

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Graph each equation of the system. Then solve the system to find the points of intersection.y=x2+1y=x+1

Short Answer

Step by step solution

Step 1. Given data

Step 2. Graph of the system of equations

Step 3. Solution of system

Step 4. Solution of system

Step 5. Verification

Step 6. Point of intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Logic and Functions

Probability and Statistics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} + 1 \\ y = x + 1 \end{cases}$