Chapter 4: Q. 341 (page 479)

In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} y = - \frac{1}{3} x + 2 \\ x + 3 y = 6 \end{cases}$

Short Answer

Expert verified

The system of linear equations has infinitely many solutions.

Step by step solution

Step 1. Given information.

The system of linear equations,

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

Step 2. Substituting the value of y from one equation into another equation.

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

Now substituting this in another equation we get

$x + 3 (- \frac{1}{3} x + 2) = 6 x - x + 6 = 6 6 = 6$

Therefore the system of linear equations has infinitely many solutions.

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In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} y = - \frac{1}{3} x + 2 \\ x + 3 y = 6 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substituting the value of y from one equation into another equation.

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In the following exercises, solve the systems of equations by substitution.y=-13x+2x+3y=6

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substituting the value of y from one equation into another equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} y = - \frac{1}{3} x + 2 \\ x + 3 y = 6 \end{cases}$