1
algebra

Is the point (4,1)(4, 1) a solution to the system? {2x+3y=11x2y=2\begin{cases} 2x + 3y = 11 \\ x - 2y = 2 \end{cases}

A

Only for the second equation

B

Yes

C

No

D

Cannot be determined

Correct Answer: B

Choice B is the correct answer. To verify if (4,1)(4, 1) is a solution, we substitute x=4x = 4 and y=1y = 1 into both equations.

First equation: 2x+3y=112x + 3y = 112(4)+3(1)=8+3=112(4) + 3(1) = 8 + 3 = 11 ✓ (True)

Second equation: x2y=2x - 2y = 242(1)=42=24 - 2(1) = 4 - 2 = 2 ✓ (True)

Since the point satisfies both equations, it is a solution to the system.

💡 Strategic Tip: A point must satisfy ALL equations to be a solution to the system.

Choice A is incorrect because the point satisfies both equations, not just the second one.

Choice C is incorrect because the point does satisfy both equations.

Choice D is incorrect because we can always determine if a point is a solution through direct substitution.