Chapter 5: Q. 397 (page 683)

In the following exercises, solve each system of equations. Use either substitution or elimination.
$y = - \frac{4}{5} x + 1 8 x + 10 y = 10$

Short Answer

Expert verified

The system has infinitely many solutions.

Step by step solution

Step 1. Given Information

In the given exercises we have to solve given system of equations using either substitution or elimination method.

$y = - \frac{4}{5} x + 1 8 x + 10 y = 10$

Step 2. y=−45x+1………………Equation 18x+10y=10………………Equation 2

Using substitution method to solve the equation.

Putting the value of y from the Equation 1 in Equation 2.

$8 x + 10 (- \frac{4}{5} x + 1) = 10 8 x + 10 \times (- \frac{4}{5}) x + 1 \times 10 = 10 8 x - 2 \times 4 x + 10 = 10 8 x - 8 x + 10 = 10 10 = 10$

Step 3. Since 10=10 is a true statement, the system is consistent.

The equations are dependent. The graphs of these two equations would give the same line. The system has infinitely many solutions.

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In the following exercises, solve each system of equations. Use either substitution or elimination.
$y = - \frac{4}{5} x + 1 8 x + 10 y = 10$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. y=−45x+1………………Equation 18x+10y=10………………Equation 2

Step 3. Since 10=10 is a true statement, the system is consistent.

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In the following exercises, solve each system of equations. Use either substitution or elimination.y=−45x+18x+10y=10

Short Answer

Step by step solution

Step 1. Given Information

Step 2. y=−45x+1………………Equation 18x+10y=10………………Equation 2

Step 3. Since 10=10 is a true statement, the system is consistent.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Geometry

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system of equations. Use either substitution or elimination.
$y = - \frac{4}{5} x + 1 8 x + 10 y = 10$