Chapter 4: Q 14 (page 385)

In the following exercises, solve the following systems of equations by graphing.
$2 x - y = 4 2 x + 3 y = 12$

Short Answer

Expert verified

The solution of the system of linear equations is (3,2).

Step by step solution

Step 1. Given information

The linear equations are

$2 x - y = 4 2 x + 3 y = 12$

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.

$2 x - y = 4 - y = - 2 x + 4 y = 2 x - 4 Here the slope is m = 2 And the y - intercept is b = - 4$

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

$2 x + 3 y = 12 3 y = - 2 x + 12 y = - \frac{2}{3} \times x + \frac{12}{3} y = - \frac{2}{3} x + 4 Here the slope is m = - \frac{2}{3} And the y - intercept is b = 4$

Step 3. Graph obtained

The solution of the system of linear equations is (3,2).

Step 4. Checking the equations

$First substitute x = 3, y = 2 into the equation 2 x - y = 4 2 (3) - 2 = 4 6 - 2 = 4 4 = 4 This is true .$

$Also substitute x = 3, y = 2 into the equation 2 x + 3 y = 12 2 x + 3 y = 12 2 (3) + 3 (2) = 12 6 + 6 = 12 12 = 12 This is true .$

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In the following exercises, solve the following systems of equations by graphing.
$2 x - y = 4 2 x + 3 y = 12$

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-y=42x+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

Logic and Functions

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve the following systems of equations by graphing.
$2 x - y = 4 2 x + 3 y = 12$