Chapter 5: Q. 40 (page 596)

In the following exercises, solve the following systems of equations by graphing.
$\{\begin{cases} x + 3 y = 4 \\ - 2 x - 6 y = 3 \end{cases}$

Short Answer

Expert verified

There is no solution of the system of equations.

Step by step solution

Step 1. Given information.

We have:

$\{\begin{cases} x + 3 y = 4 \\ - 2 x - 6 y = 3 \end{cases}$

Step 2. Find the intercepts.

We will find the x-intercept and y-intercept of both equations and use them to graph the lines.

The system of equations are:

$\{\begin{cases} x + 3 y = 4 \\ - 2 x - 6 y = 3 \end{cases}$

x-intercept: substitute $y = 0$

$x + 3 (0) = 4 x = 4$

X-intercept: $(4, 0)$

$- 2 x - 6 y = 3 x = - \frac{3}{2}$

X-intercept: $(- \frac{3}{2}, 0)$

y-intercept: substitute $x = 0$

$0 + 3 y = 4 y = \frac{4}{3}$

Y-intercept: $(0, \frac{4}{3})$

$- 2 (0) - 6 y = 3 y = - \frac{1}{2}$

Y-intercept: $(0, - \frac{1}{2})$

Step 3. Use the intercept to draw the graph.

Graph the line and find the intersection point:

The lines are parallel to each other.

Therefore, there is no intersection point.

Hence, no solution.

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In the following exercises, solve the following systems of equations by graphing.
$\{\begin{cases} x + 3 y = 4 \\ - 2 x - 6 y = 3 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the intercepts.

Step 3. Use the intercept to draw the graph.

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In the following exercises, solve the following systems of equations by graphing.x+3y=4-2x-6y=3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the intercepts.

Step 3. Use the intercept to draw the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the following systems of equations by graphing.
$\{\begin{cases} x + 3 y = 4 \\ - 2 x - 6 y = 3 \end{cases}$