Chapter 5: Q 5.20. (page 591)

Without graphing, determine the number of solutions and then classify the system of equations.
$x + 4 y = 12 - x + y = 3$

Short Answer

Expert verified

The system of the equation has 1 solution and is consistent and independent.

Step by step solution

Step 1. Given information

The system of equations is

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

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

The first equation is

$x + 4 y = 12$

Solve for $y$

$x + 4 y = 12 x + 4 y - x = 12 - x 4 y = - x + 12 \frac{4 y}{4} = - \frac{1}{4} x + \frac{12}{4} y = - \frac{1}{4} x + 3$

Compare with the slope-intercept formula of line

$y = m x + b$

So,

$m = - \frac{1}{4} b = 3$

Step 3. Find the slope and intercept of the second equation.

The second equation is

$- x + y = 3$

Solve for $y$

$- x + y = 3 - x + y + x = 3 + x y = x + 3$

Compare with the slope-intercept formula of line

$y = m x + b$

So,

$m = 1 b = 3$

Step 4. Compare the slopes and intercepts of the two lines.

First equation:

Slope is $- \frac{1}{4}$

y-intercept is $3$

Second equation:

Slope is $1$

y-intercept is $3$

Since the slopes are different, the lines intersect.

A system of equations whose graphs are intersecting has 1 solution and is consistent and independent.

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Without graphing, determine the number of solutions and then classify the system of equations.
$x + 4 y = 12 - x + y = 3$

Short Answer

Step by step solution

Step 1. Given information

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

Step 3. Find the slope and intercept of the second equation.

Step 4. Compare the slopes and intercepts of the two lines.

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Without graphing, determine the number of solutions and then classify the system of equations.x+4y=12-x+y=3

Short Answer

Step by step solution

Step 1. Given information

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

Step 3. Find the slope and intercept of the second equation.

Step 4. Compare the slopes and intercepts of the two lines.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Geometry

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Without graphing, determine the number of solutions and then classify the system of equations.
$x + 4 y = 12 - x + y = 3$