Chapter 5: Q. 26 (page 595)

In the following exercises, solve the following systems of equations by graphing.
$\{\begin{cases} x + y = 4 \\ x - y = 0 \end{cases}$

Short Answer

Expert verified

The solutions to the system of equations are $x = 2$ and $y = 2$ .

Step by step solution

Step 1. Given information.

We have:

$\{\begin{cases} x + y = 4 \\ x - y = 0 \end{cases}$

Step 2. Find the intercepts.

We will find the x-intercept and y-intercept of both equations and use them to graph the lines.

The system of equations are:

$\{\begin{cases} x + y = 4 \\ x - y = 0 \end{cases}$

x-intercept: substitute $y = 0$

$x + 0 = 4 x = 4$

X-intercept: $(4, 0)$

$x - 0 = 0 x = 0$

X-intercept: $(0, 0)$

y-intercept: substitute $x = 0$

$0 + y = 4 y = 4$

Y-intercept: $(0, 4)$

$0 - y = 0 y = 0$

Y-intercept: $(0, 0)$

Step 3. Use the intercept to draw the graph.

Graph the line and find the intersection point:

The lines intersect at $(2, 2)$ .

Therefore, the solutions are:

$x = 2, y = 2$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, solve the following systems of equations by graphing.
$\{\begin{cases} x + y = 4 \\ x - y = 0 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the intercepts.

Step 3. Use the intercept to draw the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the following systems of equations by graphing.x+y=4x-y=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the intercepts.

Step 3. Use the intercept to draw the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the following systems of equations by graphing.
$\{\begin{cases} x + y = 4 \\ x - y = 0 \end{cases}$