Chapter 4: Q 39. (page 386)

Solve the system of equations by substitution
$\{\begin{cases} 4 x + y = 10 \\ x - 2 y = - 20 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations is,

$x = 0 y = 10$

Step by step solution

Step 1. Given the information

The system of equations is,

$\{\begin{cases} 4 x + y = 10 \\ x - 2 y = - 20 \end{cases}$

Step 2. Solve the first equation for y.

Solving the equation $4 x + y = 10$ for $y$

$4 x + y = 10$

$y = 10 - 4 x$

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

Substituting $y = 10 - 4 x$ in the equation

$x - 2 y = - 20$

$x - 2 (10 - 4 x) = - 20$

$x - 20 + 8 x = - 20$

$9 x - 20 = - 20$

$9 x = - 20 + 20$

$9 x = 0$

$x = 0 \div 9$

$x = 0$

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

Substituting $x = 0$ in the equation

$y = 10 - 4 x$

$y = 10 - 4 (0)$

$y = 10 - 0$

$y = 10$

Step 5. Checking the solution for the equation 4x+y=10

Substituting $x = 0 y = 10$ in the equation

$4 x + y = 10$

$4 (0) + 10 = 10$

$0 + 10 = 10$

$10 = 10$

This is true.

Step 6. Checking the solution for the equation x-2y=-20

Substituting $x = 0 y = 10$ in the equation

$x - 2 y = - 20$

$0 - 2 (10) = - 20$

$0 - 20 = - 20$

$- 20 = - 20$

This is true.

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Solve the system of equations by substitution
$\{\begin{cases} 4 x + y = 10 \\ x - 2 y = - 20 \end{cases}$

Short Answer

Step by step solution

Step 1. Given the information

Step 2. Solve the first equation for y.

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

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

Step 5. Checking the solution for the equation 4x+y=10

Step 6. Checking the solution for the equation x-2y=-20

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Solve the system of equations by substitution4x+y=10x-2y=-20

Short Answer

Step by step solution

Step 1. Given the information

Step 2. Solve the first equation for y.

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

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

Step 5. Checking the solution for the equation 4x+y=10

Step 6. Checking the solution for the equation x-2y=-20

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Geometry

Pure Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the system of equations by substitution
$\{\begin{cases} 4 x + y = 10 \\ x - 2 y = - 20 \end{cases}$