Q 35 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 35 (page 386)

Solve the system of equations by substitution
$\{\begin{cases} - 2 x + 2 y = 6 \\ y = - 3 x + 1 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations is,

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

Step by step solution

Step 1. Given information

The system of equations is,

$\{\begin{cases} - 2 x + 2 y = 6 \\ y = - 3 x + 1 \end{cases}$

Step 2. Substituting the value of y in the equation.

Substitute $y = - 3 x + 1$ in the equation

$- 2 x + 2 y = 6$ ,

$- 2 x + 2 (- 3 x + 1) = 6$

$- 2 x - 6 x + 2 = 6$

$- 8 x + 2 = 6$

$- 8 x = 6 - 2$

$- 8 x = 4$

$x = - \frac{4}{8}$

$x = \frac{- 1}{2}$

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

Substituting the value of $x = - \frac{1}{2}$ in the equation

$y = - 3 x + 1$

$y = - 3 (- \frac{1}{2}) + 1$

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

$y = \frac{3 + 2}{2}$

$y = \frac{5}{2}$

Step 4. Checking the solution for the equation y=-3x+1

Substituting $x = - \frac{1}{2} y = \frac{5}{2}$ in the equation

$y = - 3 x + 1$

$\frac{5}{2} = - 3 (- \frac{1}{2}) + 1$

$\frac{5}{2} = \frac{3}{2} + 1$

$\frac{5}{2} = \frac{3 + 2}{2}$

$\frac{5}{2} = \frac{5}{2}$

This is true.

Step 5. Checking the solution for the equation -2x+2y=6.

Substituting $x = - \frac{1}{2}, y = \frac{5}{2}$ in the equation

$- 2 x + 2 y = 6$

$- 2 (- \frac{1}{2}) + 2 (\frac{5}{2}) = 6$

$1 + 5 = 6$

$6 = 6$

This is true.

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91影视

Solve the system of equations by substitution
$\{\begin{cases} - 2 x + 2 y = 6 \\ y = - 3 x + 1 \end{cases}$

Short Answer

Step by step solution

Step 1. Given 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=-3x+1

Step 5. Checking the solution for the equation -2x+2y=6.

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91影视

Solve the system of equations by substitution-2x+2y=6y=-3x+1

Short Answer

Step by step solution

Step 1. Given 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=-3x+1

Step 5. Checking the solution for the equation -2x+2y=6.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Statistics

Study anywhere. Anytime. Across all devices.

Solve the system of equations by substitution
$\{\begin{cases} - 2 x + 2 y = 6 \\ y = - 3 x + 1 \end{cases}$