Chapter 4: Q 330 (page 479)

In the following exercises, solve the following system of equations by graphing
$3 x + y = 6 x + 3 y = - 6$

Short Answer

Expert verified

The solution to the linear equations is (3,-3).

Step by step solution

Step 1. Given information

The given linear equations are

$3 x + y = 6 x + 3 y = - 6$

Step 2. Finding the intersecting points

First, solve both of these equations for y such that their slopes and y intercepts may be easily graphed.

And find the slope and y-intercept by solving the first equation for y.

$Solve the first equation for y . and find the slope and y - intercept . 3 x + y = 6 y = - 3 x + 6 Here the slope is m = - 3 And the y - intercept is b = 6$

Again find the slope and y-intercept by solving the Second equation for y.

$x + 3 y = - 6 3 y = - x - 6 y = - \frac{1}{3} x - 2 Here the slope is m = - \frac{1}{3} And the y - intercept is b = - 2$ $x + 3 y = - 6 3 y = - x - 6 y = - \frac{1}{3} x - 2 Here the slope i s m = - \frac{1}{3} And the y - intercept is b = - 2$

Step 3. The graph obtained

$Check : First substitute x = 3, y = - 3 into the equation 3 x + y = 6 3 x + y = 6 3 (3) - 3 = 6 9 - 3 = 6 6 = 6 This is true . Also substitute x = 3, y = - 3 into the equatio n x + 3 y = - 6 x + 3 y = - 6 3 + 3 (- 3) = - 6 3 - 9 = - 6 - 6 = - 6 This is true .$

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 system of equations by graphing
$3 x + y = 6 x + 3 y = - 6$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the intersecting points

Step 3. The graph obtained

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Pure Maths

Decision Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the following system of equations by graphing3x+y=6x+3y=-6

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the intersecting points

Step 3. The graph obtained

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Pure Maths

Decision Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the following system of equations by graphing
$3 x + y = 6 x + 3 y = - 6$