Chapter 5: Q 5.16. (page 588)

Solve each system by graphing:
$y = \frac{1}{2} x - 4 2 x - 4 y = 16$

Short Answer

Expert verified

There are infinitely many solutions to this system.

Step by step solution

Step 1. Given information

The system of equations is

$y = \frac{1}{2} x - 4 2 x - 4 y = 16$

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

The first equation is

$y = \frac{1}{2} x - 4$

Compare with the slope-intercept formula of a line

$y = m x + b$

So,

$m = \frac{1}{2} b = - 4$

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

The second equation is

$2 x - 4 y = 16$

x-intercept:

$2 x - 4 \times 0 = 16 2 x - 0 = 16 2 x = 16 \frac{2 x}{2} = \frac{16}{2} x = 8$

So, the x-intercept is $(8, 0)$

y-intercept:

$2 \times 0 - 4 y = 16 - 4 y = 16 \frac{- 4 y}{- 4} = \frac{16}{- 4} y = - 4$

So, the y-intercept is $(0, - 4)$

Step 4. Graph the two lines.

First equation:

Slope is $\frac{1}{2}$

y-intercept is $(0, - 4)$

Second equation:

Locate points $(8, 0), (0, - 4)$ on the graph and then join them to get the graph

So, the graph is

Step 5. Determine the point of intersection

The graph is

The lines are the same!

Since every point on the line makes both equations true,

there are infinitely many ordered pairs that make both equations true.

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Solve each system by graphing:
$y = \frac{1}{2} x - 4 2 x - 4 y = 16$

Short Answer

Step by step solution

Step 1. Given information

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

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

Step 4. Graph the two lines.

Step 5. Determine the point of intersection

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Solve each system by graphing:y=12x-42x-4y=16

Short Answer

Step by step solution

Step 1. Given information

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

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

Step 4. Graph the two lines.

Step 5. Determine the point of intersection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Decision Maths

Statistics

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each system by graphing:
$y = \frac{1}{2} x - 4 2 x - 4 y = 16$