Chapter 4: Q 36. (page 386)

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

Short Answer

Expert verified

The solution for the system of equations is,

$x = 3 y = - 1$ .

Step by step solution

Step 1. Given information

The system of equations is,

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

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

Substitute $y = \frac{1}{3} x - 2$ in the equation

$2 x + 5 y = 1$

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

role="math" localid="1644341510028" $2 x + \frac{5}{3} x - 10 = 1$

$2 x + \frac{5 x}{3} = 1 + 10$

$\frac{6 x + 5 x}{3} = 11$

$\frac{11 x}{3} = 11$

$x = 11 \div \frac{11}{3}$

$x = 11 \times \frac{3}{11}$

$x = 3$

Step 3. Substituting the value of x in the equation

Substituting the value of $x = 3$ in the equation

$y = \frac{1}{3} x - 2$

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

$y = 1 - 2$

$y = - 1$

Step 4. Checking the solution for the equation 2x+5y=1

Substituting $x = 3 y = - 1$ in the equation

$2 x + 5 y = 1$

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

$6 + (- 5) = 1$

$6 - 5 = 1$

$1 = 1$

This is true.

Step 5. Checking the solution for the equation y=13x-2

Substituting $x = 3 y = - 1$ in the equation

$y = \frac{1}{3} x - 2$

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

$- 1 = 1 - 2$

$- 1 = - 1$

This is true.

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

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 2x+5y=1

Step 5. Checking the solution for the equation y=13x-2

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Solve the system of equations by substitution2x+5y=1y=13x-2

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 2x+5y=1

Step 5. Checking the solution for the equation y=13x-2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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