Chapter 4: Q 37. (page 386)

Solve the system of equations by substitution
$\{\begin{cases} 3 x + 4 y = 1 \\ y = - \frac{2}{5} x + 2 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations is,

$x = - 5 y = 4$

Step by step solution

Step 1. Given the information

The system of equations is,

$\{\begin{cases} 3 x + 4 y = 1 \\ y = - \frac{2}{5} x + 2 \end{cases}$

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

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

$3 x + 4 y = 1$

role="math" localid="1644342937459" $3 x + 4 (- \frac{2}{5} x + 2) = 1$

$3 x - \frac{8}{5} x + 8 = 1$

$3 x - \frac{8 x}{5} = 1 - 8$

$\frac{15 x - 8 x}{5} = - 7$

$\frac{7 x}{5} = - 7$

$x = - 7 \div \frac{7}{5}$

$x = - 7 \times \frac{5}{7}$

$x = - 5$

Step 3. Substituting the value of x in the equation

Substituting $x = - 5$ in the equation

$y = - \frac{2}{5} x + 2$

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

$y = 2 + 2$

$y = 4$

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

Substituting $x = - 5 y = 4$ in the equation

$3 x + 4 y = 1$

$3 (- 5) + 4 (4) = 1$

$- 15 + 16 = 1$

$1 = 1$

This is true

Step 5. Checking the solution for the equation y=-25x+2

Substituting $x = - 5 y = 4$ in the equation

$y = - \frac{2}{5} x + 2$

$4 = - \frac{2}{5} (- 5) + 2$

$4 = 2 + 2$

$4 = 4$

This is true.

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Solve the system of equations by substitution
$\{\begin{cases} 3 x + 4 y = 1 \\ y = - \frac{2}{5} x + 2 \end{cases}$

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 3x+4y=1

Step 5. Checking the solution for the equation y=-25x+2

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Solve the system of equations by substitution3x+4y=1y=-25x+2

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 3x+4y=1

Step 5. Checking the solution for the equation y=-25x+2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Applied Mathematics

Geometry

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve the system of equations by substitution
$\{\begin{cases} 3 x + 4 y = 1 \\ y = - \frac{2}{5} x + 2 \end{cases}$