Chapter 4: Q 25. (page 386)

Without graphing, determine the number of solutions and then classify the system of equations.
$\{\begin{cases} y = \frac{2}{3} x + 1 \\ - 2 x + 3 y = 5 \end{cases}$

Short Answer

Expert verified

The number of solutions is 0 and the system of equations are parallel lines, inconsistent and independent.

Step by step solution

Step 1. Given information.

The system of equations is $\{\begin{cases} y = \frac{2}{3} x + 1 \\ - 2 x + 3 y = 5 \end{cases}$ .

Step 2. Solve the first equation for y.

Find the slope andy-intercept.

y = \frac{2}{3} x + 1

Hence the slope is $\frac{2}{3}$ and the y-intercept is 1.

Step 3. Solve the second equation for y.

Find the slope and y-intercept.

- 2 x + 3 y = 5 y = \frac{2}{3} x + \frac{5}{3}

Hence the slope is $\frac{2}{3}$ and the y-intercept is $\frac{5}{3}$ .

Step 4. Explain the number of solutions.

Here the slopes are the same and y-intercepts are different.
The system of equations are parallel lines, inconsistent and independent and the number of solutions is 0.

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Without graphing, determine the number of solutions and then classify the system of equations.
$\{\begin{cases} y = \frac{2}{3} x + 1 \\ - 2 x + 3 y = 5 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the first equation for y.

Step 3. Solve the second equation for y.

Step 4. Explain the number of solutions.

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Without graphing, determine the number of solutions and then classify the system of equations.y=23x+1-2x+3y=5

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the first equation for y.

Step 3. Solve the second equation for y.

Step 4. Explain the number of solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Statistics

Probability and Statistics

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Geometry

Study anywhere. Anytime. Across all devices.

Without graphing, determine the number of solutions and then classify the system of equations.
$\{\begin{cases} y = \frac{2}{3} x + 1 \\ - 2 x + 3 y = 5 \end{cases}$