Chapter 6: Q13. (page 389)

Graph each system and determine the number of solutions that it has. If it has one solution, name it.
$\begin{array}{l} 2 x - 3 y = - 6 \\ y = - 3 x + 2 \end{array}$

Short Answer

Expert verified

The graph of the system is

The number of solutions is 1 and name of the solution is $(0, 2)$ .

Step by step solution

Step 1. Graph the system of equations.

The given system of equation is:

$2 x - 3 y = - 6$ … (1)

$y = - 3 x + 2$ … (2)

The graph of two equations is drawn as below.

Step 2. Determine the number of solutions.

From the graph it can be observed that the two lines intersect at exactly one point. This intersection point of two lines is nothing but the solution set of given system of equation. Therefore, number of solutions of the set of equations if 1.

Step 3. Name the solutions, if possible.

Now the intersection point of two straight lines shown by eq. (1) and (2) is $(0, 2)$ . Therefore, one solution of given system of equation is labelled as $(0, 2)$ .

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Graph each system and determine the number of solutions that it has. If it has one solution, name it.
$\begin{array}{l} 2 x - 3 y = - 6 \\ y = - 3 x + 2 \end{array}$

Short Answer

Step by step solution

Step 1. Graph the system of equations.

Step 2. Determine the number of solutions.

Step 3. Name the solutions, if possible.

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Graph each system and determine the number of solutions that it has. If it has one solution, name it.2x−3y=−6y=−3x+2

Short Answer

Step by step solution

Step 1. Graph the system of equations.

Step 2. Determine the number of solutions.

Step 3. Name the solutions, if possible.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Discrete Mathematics

Geometry

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Graph each system and determine the number of solutions that it has. If it has one solution, name it.
$\begin{array}{l} 2 x - 3 y = - 6 \\ y = - 3 x + 2 \end{array}$