Q 13 In the following exercises, solv... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q 13 (page 385)

In the following exercises, solve the following systems of equations by graphing.
$- 2 x + 3 y = 3 x + 3 y = 12$

Short Answer

Expert verified

The solution of the system of linear equations is (3,3).

Step by step solution

Step 1. Given information.

Two linear equations are,

$- 2 x + 3 y = 3 x + 3 y = 12$

Step 2. Solving equations for the intersection 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.

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

$\begin{array}{rcl} - 2 x + 3 y & = & 3 \\ 3 y & = & 3 + 2 x \\ y & = & \frac{3}{3} + \frac{2}{3} x \\ y & = & \frac{2}{3} 脳 x + 1 \\ Here the slope is m & = & \frac{2}{3} \\ And the y - intercept is b & = & 1 \end{array}$

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

$x + 3 y = 12 3 y = - x + 12 y = - \frac{1}{3} 脳 x + \frac{12}{3} y = - \frac{1}{3} 脳 x + 4 Here the slope is m = - \frac{1}{3} And the y - intercept is b = 4$

Step 3. Graph obtained.

Step 4. Checking the equations

$First substitute x = 3, y = 3 into the equation - 2 x + 3 y = 3 - 2 x + 3 y = 3 - 2 脳 3 + 3 (3) = 3 - 6 + 9 = 3 3 = 3 This is true .$

$First substitute x = 3, y = 3 into the equation x + 3 y = 12 x + 3 y = 12 3 + 3 (3) = 12 3 + 9 = 12 12 = 12 This is true .$

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91影视

In the following exercises, solve the following systems of equations by graphing.
$- 2 x + 3 y = 3 x + 3 y = 12$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving equations for the intersection points

Step 3. Graph obtained.

Step 4. Checking the equations

One App. One Place for Learning.

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91影视

In the following exercises, solve the following systems of equations by graphing.-2x+3y=3x+3y=12

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving equations for the intersection points

Step 3. Graph obtained.

Step 4. Checking the equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Mechanics Maths

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the following systems of equations by graphing.
$- 2 x + 3 y = 3 x + 3 y = 12$