Chapter 4: Q 28 (page 386)

Without graphing, determine the number of solutions and then classify the system of equations.
$y = - \frac{1}{2} x + 5 x + 2 y = 10$

Short Answer

Expert verified

The number of solution is infinite and the system of equations is coincident lines, consistent and dependent.

Step by step solution

Step 1. Given information

The system of equations is $\{\begin{cases} y = - \frac{1}{2} x + 5 \\ x + 2 y = 10 \end{cases}$

Step 2. Solve the first equation for y and find the slope and y-intercept.

$y = - \frac{1}{2} x + 5$

Here the slope is $- \frac{1}{2}$

And the $y$ -intercept is $5$

Step 3. Solve the second equation for y and find the slope and y-intercept.

$x + 2 y = 10 2 y = 10 - x y = - \frac{1}{2} x + 5$

Here the slope is $- \frac{1}{2}$

And the $y$ -intercept is $5$

Step 4. Required answer

Here the slopes and $y$ -intercepts are same.

Therefore, the system of equation is coincident lines with infinite solution and is consistent and dependent.

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Without graphing, determine the number of solutions and then classify the system of equations.
$y = - \frac{1}{2} x + 5 x + 2 y = 10$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the first equation for y and find the slope and y-intercept.

Step 3. Solve the second equation for y and find the slope and y-intercept.

Step 4. Required answer

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Without graphing, determine the number of solutions and then classify the system of equations.y=-12x+5x+2y=10

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the first equation for y and find the slope and y-intercept.

Step 3. Solve the second equation for y and find the slope and y-intercept.

Step 4. Required answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Without graphing, determine the number of solutions and then classify the system of equations.
$y = - \frac{1}{2} x + 5 x + 2 y = 10$