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.

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

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

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

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

Step 3. Graph obtained.

Step 4. Checking the equations

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

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

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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

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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

Statistics

Decision Maths

Discrete Mathematics

Calculus

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

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