Q 40. Solve the system of equations by... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q 40. (page 386)

Solve the system of equations by substitution
$\{\begin{cases} y = - 2 x - 1 \\ y = - \frac{1}{3} x + 4 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations is,

$x = - 3 y = 5$

Step by step solution

Step 1. Given the information

The system of equations is,

$\{\begin{cases} y = - 2 x - 1 \\ y = - \frac{1}{3} x + 4 \end{cases}$

Step 2. Substituting the value of y in the equation

Substituting $y = - 2 x - 1$ in the equation

$y = - \frac{1}{3} x + 4$

$- 2 x - 1 = - \frac{1}{3} x + 4$

role="math" localid="1644347591540" $- 2 x + \frac{1}{3} x = 4 + 1$

$\frac{- 6 x + x}{3} = 5$

$\frac{- 5 x}{3} = 5$

$x = 5 梅 \frac{- 5}{3}$

$x = 5 脳 \frac{- 3}{5}$

$x = - 3$

Step 3. Substituting the value of x in the equation.

Substituting $x = - 3$ in the equation

$y = - 2 x - 1$

$y = - 2 (- 3) - 1$

$y = 6 - 1$

$y = 5$

Step 4. Checking the solution for the equation y=-2x-1

Substituting $x = - 3 y = 5$ in the equation

$y = - 2 x - 1$

$5 = - 2 (- 3) - 1$

$5 = 6 - 1$

$5 = 5$

This is true.

Step 5. Checking the solution for the equation y=-13x+4

Substituting $x = - 3 y = 5$ in the equation

$y = - \frac{1}{3} x + 4$

$5 = - \frac{1}{3} (- 3) + 4$

$5 = 1 + 4$

$5 = 5$

This is true.

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91影视

Solve the system of equations by substitution
$\{\begin{cases} y = - 2 x - 1 \\ y = - \frac{1}{3} x + 4 \end{cases}$

Short Answer

Step by step solution

Step 1. Given the information

Step 2. Substituting the value of y in the equation

Step 3. Substituting the value of x in the equation.

Step 4. Checking the solution for the equation y=-2x-1

Step 5. Checking the solution for the equation y=-13x+4

One App. One Place for Learning.

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91影视

Solve the system of equations by substitutiony=-2x-1y=-13x+4

Short Answer

Step by step solution

Step 1. Given the information

Step 2. Substituting the value of y in the equation

Step 3. Substituting the value of x in the equation.

Step 4. Checking the solution for the equation y=-2x-1

Step 5. Checking the solution for the equation y=-13x+4

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

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Mechanics Maths

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the system of equations by substitution
$\{\begin{cases} y = - 2 x - 1 \\ y = - \frac{1}{3} x + 4 \end{cases}$