Given the equation $2x+3y=10$ what is the missing variable shown below?


(__, $-\frac{5}{3}$)

• A. $-\frac{20}{3}$
• B. $\frac{10}{3}$
• C. $\frac{15}{2}$
• D. $-\frac{15}{2}$

Answer: (C)

Verified step by step guidance

1. Identify the given equation: \(2x + 3y = 10\).
2. Note the given point has the form \((\_, -\frac{5}{3})\), where the \(y\)-coordinate is \(-\frac{5}{3}\) and the \(x\)-coordinate is unknown.
3. Substitute \(y = -\frac{5}{3}\) into the equation: \(2x + 3\left(-\frac{5}{3}\right) = 10\).
4. Simplify the equation after substitution: \(2x - 5 = 10\).
5. Solve for \(x\) by isolating it: add 5 to both sides to get \(2x = 15\), then divide both sides by 2 to find \(x = \frac{15}{2}\).