Chapter 6: Q. 300 (page 627)

In the following exercises, solve:
$(2 y - 3) (3 y - 1) = 8 y$

Short Answer

Expert verified

On solving the equation, we get $y = \frac{1}{6}, 3$ .

Step by step solution

Step 1. Given information.

Consider the given equation,

$(2 y - 3) (3 y - 1) = 8 y$

Write the quadratic equation in standard form,

$6 y^{2} - 2 y - 9 y - 8 y + 3 = 0 6 y^{2} - 19 y + 3 = 0$

Step 2. Factor the quadratic expression.

On factoring, we get,

$6 y^{2} - 18 y - y + 3 = 0 6 y (y - 3) - (y - 3) = 0 (6 y - 1) (y - 3) = 0$

Use the zero product property,

$6 y - 1 = 0 y = \frac{1}{6}$

Then,

$y - 3 = 0 y = 3$

Step 3. Check the answers.

Substitute $y = \frac{1}{6}$ in the given equation,

$(2 (\frac{1}{6}) - 3) (3 (\frac{1}{6}) - 1) = 8 (\frac{1}{6}) (\frac{1}{3} - 3) (\frac{1}{2} - 1) = \frac{4}{3} (\frac{- 8}{3}) (\frac{- 1}{2}) = \frac{4}{3} \frac{4}{3} = \frac{4}{3}$

This is true.

Substitute $y = 3$ in the given equation,

$(2 (3) - 3) (3 (3) - 1) = 8 (3) (6 - 3) (9 - 1) = 8 (3) (3) (8) = 8 (3) 24 = 24$

This is also true.

Hence, the answer is $y = \frac{1}{6}, 3$ .

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In the following exercises, solve:
$(2 y - 3) (3 y - 1) = 8 y$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor the quadratic expression.

Step 3. Check the answers.

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In the following exercises, solve:2y-33y-1=8y

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor the quadratic expression.

Step 3. Check the answers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, solve:
$(2 y - 3) (3 y - 1) = 8 y$