Chapter 4: Q. 407 (page 485)

In the following exercises, solve the following systems by graphing.
$\{\begin{cases} x - y = 5 \\ x + 2 y = - 4 \end{cases}$

Short Answer

Expert verified

The solution of the system of the equation $\{\begin{cases} x - y = 5 \\ x + 2 y = - 4 \end{cases}$ is the point of intersection $(2, - 3)$

Step by step solution

Step 1. Given

The system of equation is $\{\begin{cases} x - y = 5 \\ x + 2 y = - 4 \end{cases}$

To find the solution of equation by graphing

Step 2. Find slope and y-intercept of first equation

Write the equation in the form of

$x - y = 5$

$y = x - 5$ which is the slope-intercept form.

So, slope $m = 1$ and

$b = - 5$

Step 3. Find slope and y-intercept of the second equation

Write the equation in the form of $y = m x + b$

$x + 2 y = - 4$

$2 y = - 4 - x$

$y = \frac{- 4 - x}{2}$

which is the slope-intercept form.

So, slope $m = - \frac{1}{2}$ and

$b = - 2$

Step 4. Graph the lines

Graph the equation $x - y = 5$ and

$x + 2 y = - 4$

And find the point of intersection.

The point of intersection is $(2, - 3)$

Step 5. Check the solution

Substitute the point $(2, - 3)$ in the equation,

$x - y = 5$

$2 - (- 3) = 5$

$5 = 5$ is true.

Substitute the point $(2, - 3)$ in the equation,

$x + 2 y = - 4$

$2 + 2 (- 3) = - 4$

$2 - 6 = - 4$

$- 4 = - 4$ is true.

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 by graphing.
$\{\begin{cases} x - y = 5 \\ x + 2 y = - 4 \end{cases}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Find slope and y-intercept of first equation

Step 3. Find slope and y-intercept of the second equation

Step 4. Graph the lines

Step 5. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Calculus

Decision Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the following systems by graphing.x-y=5x+2y=-4

Short Answer

Step by step solution

Step 1. Given

Step 2. Find slope and y-intercept of first equation

Step 3. Find slope and y-intercept of the second equation

Step 4. Graph the lines

Step 5. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Calculus

Decision Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the following systems by graphing.
$\{\begin{cases} x - y = 5 \\ x + 2 y = - 4 \end{cases}$