Question

select the correct answer from the drop-down menu.

the equation choose an answer has no solution.

options in drop-down:
13y + 2 - 2y = 10y + 3 - y
9(3y + 7) - 2 = 3(-9y + 9)
32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1
5(2.2y + 3.4) = 5(y - 2) + 6y

Explanation:

Analyze the condition for no solution

Using the Number of Solutions knowledge point

A linear equation in the form \(ay + b = cy + d\) has no solution if and only if the coefficients of the variable are equal (\(a = c\)) but the constant terms are different (\(b
eq d\)). This simplifies to an impossible statement like \(0 = \text{non-zero constant}\).

Test the first equation

Using the Linear Equations knowledge point

$$
LATEXBLOCK0
$$

This equation has exactly one solution: \(y = \frac{1}{2}\).

Test the second equation

Using the Linear Equations knowledge point

$$
LATEXBLOCK1
$$

This equation has exactly one solution: \(y = -\frac{17}{27}\).

Test the third equation

Using the Linear Equations knowledge point

$$
LATEXBLOCK2
$$

This equation has infinitely many solutions.

Test the fourth equation

Using the Linear Equations knowledge point

$$
LATEXBLOCK3
$$

Since \(17
eq -10\), this equation has no solution.

Answer:

• (A) \(13y + 2 - 2y = 10y + 3 - y\)
• (B) \(9(3y + 7) - 2 = 3(-9y + 9)\)
• (C) \(32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1\)
• (D) \(5(2.2y + 3.4) = 5(y - 2) + 6y\) (Correct answer)