Try multiplying the entire given equation $\frac{3}{2}x + 5y = 20$ by 2 so you can compare it more easily to the answer choices.

After rewriting the first equation, compare the coefficients of $x$ and $y$ and the constant term to each answer choice. Which choice has $x$ and $y$ coefficients in the same ratio as the first equation but a different constant term?

In Desmos, type the given equation as 3/2x + 5y = 20 (or (3/2)x + 5y = 20). This plots the first line.

Type each answer choice as a separate equation, for example 3x + 10y = 40, then 3x + 10y = 30, then the others. For each one, see how its line relates to the original line.

In Desmos:

• If the new line overlaps exactly with the original, the system has infinitely many solutions.
• If the new line crosses the original at exactly one point, the system has one solution.
• If the new line is parallel and never meets the original, the system has no solution.

Identify the choice whose line is parallel to the original and never intersects it; that is the one that makes the system have no solution.

For two linear equations in $x$ and $y$:

• One solution: lines intersect in exactly one point (different slopes).
• Infinitely many solutions: lines are the same (all coefficients and constants are proportional).
• No solution: lines are parallel but different (the $x$ and $y$ coefficients are proportional, but the constants are not).

The given equation is

To clear the fraction, multiply every term by 2:

So the first line can be written as $3x + 10y = 40$.

For the system to have no solution, the second equation must represent a line that is parallel to but different from $3x + 10y = 40$.

That means:

• The coefficients of $x$ and $y$ must be in the same ratio as $3$ and $10$ (so the line has the same slope).
• The constant term must be different from 40 (so it is not the same line).

Look for an answer choice where the left-hand side matches $3x + 10y$ (or is a constant multiple of it), but the number on the right side is not $40$.

Among the choices, $3x + 10y = 30$ has the same $x$ and $y$ coefficients as $3x + 10y = 40$ but a different constant term.

So this second equation is parallel to the first line but not the same line, which makes the system have no solution.

Therefore, the correct answer is $3x + 10y = 30$. (Choice B)