Q 4.10 Solve the system by graphing: 聽... [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 4.10 (page 374)

Solve the system by graphing: $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$

Short Answer

Expert verified

The system of equations $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$ has infinitely many solutions and it can be seen in the graph as

Step by step solution

Step 1. Given Information.

We are given a system of equations $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$ and we need to find its solution by graphing.

Step 2. Graph the first equation.

The equation $y = \frac{1}{2} x - 4$ is in slope-intercept form, so its slope is $\frac{1}{2}$ and its $y$ intercept is $- 4$ .

So its graph is given as,

Step 3. Graph the second equation on the same rectangular coordinate system.

Solving the equation $2 x - 4 y = 16$ for $y$ we get,

localid="1644388026323" $\begin{array}{rcl} 2 x - 4 y - 2 x & = & 16 - 2 x \\ - 4 y & = & - 2 x + 16 \\ \frac{- 4 y}{- 4} & = & \frac{- 2 x + 16}{- 4} \\ y & = & \frac{1}{2} x - 4 \end{array}$

So the slope of the line is $\frac{1}{2}$ and its $y$ intercept is $- 4$ .

So its graph can be drawn on the same plane as,

Step 4. Identify the solution to the system.

From the graph, it can be seen that the graph of the equations is the same.
Since every point on the line makes both equations true, there are infinitely many ordered pairs that make both equations true.
There are infinitely many solutions to this system.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve the system by graphing: $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Graph the first equation.

Step 3. Graph the second equation on the same rectangular coordinate system.

Step 4. Identify the solution to the system.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Calculus

Probability and Statistics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

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

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Graph the first equation.

Step 3. Graph the second equation on the same rectangular coordinate system.

Step 4. Identify the solution to the system.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Calculus

Probability and Statistics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve the system by graphing: $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$