Chapter 4: Q 43. (page 386)

Solve the system of equations by substitution
$\{\begin{cases} 2 x - 16 y = 8 \\ - x - 8 y = - 4 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations is,

$x = 4 y = 0$ .

Step by step solution

Step 1. Given the information

The system of equations is,

$\{\begin{cases} 2 x - 16 y = 8 \\ - x - 8 y = - 4 \end{cases}$

Step 2. Finding the value of x from the first equation.

Using the equation $2 x - 16 y = 8$ to find the value of $x$ .

$2 x - 16 y = 8$

$2 (x - 8 y) = 8$

$x - 8 y = 4$

$x = 4 + 8 y$

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

Substituting $x = 4 + 8 y$ in the equation

$- x - 8 y = - 4$

$- (4 + 8 y) - 8 y = - 4$

$- 4 - 8 y - 8 y = - 4$

$- 16 y - 4 = - 4$

$- 16 y = - 4 + 4$

$- 16 y = 0$

$y = 0 \div (- 16)$

$y = 0$

Step 4. Substituting the value of y in the equation.

Substituting $y = 0$ in the equation

$x = 4 + 8 y$ .

$x = 4 + 8 (0)$

$x = 4 + 0$

$x = 4$

Step 5. Checking the solution for the equation 2x-16y=8

Substituting $x = 4 y = 0$ in the equation

$2 x - 16 y = 8$

$2 (4) - 16 (0) = 8$

$8 - 0 = 8$

$8 = 8$

This is true.

Step 6. Checking the solution for the equation -x-8y=-4.

Substituting $x = 4 y = 0$ in the equation

$- x - 8 y = - 4$

$- 4 - 8 (0) = - 4$

$- 4 - 0 = - 4$

$- 4 = - 4$

This is true.

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Solve the system of equations by substitution
$\{\begin{cases} 2 x - 16 y = 8 \\ - x - 8 y = - 4 \end{cases}$

Short Answer

Step by step solution

Step 1. Given the information

Step 2. Finding the value of x from the first equation.

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

Step 4. Substituting the value of y in the equation.

Step 5. Checking the solution for the equation 2x-16y=8

Step 6. Checking the solution for the equation -x-8y=-4.

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Solve the system of equations by substitution2x-16y=8-x-8y=-4

Short Answer

Step by step solution

Step 1. Given the information

Step 2. Finding the value of x from the first equation.

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

Step 4. Substituting the value of y in the equation.

Step 5. Checking the solution for the equation 2x-16y=8

Step 6. Checking the solution for the equation -x-8y=-4.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

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Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Solve the system of equations by substitution
$\{\begin{cases} 2 x - 16 y = 8 \\ - x - 8 y = - 4 \end{cases}$