1
algebra

Is the point (1,8)(1, 8) a solution to the system? {2x+y=105xy=3\begin{cases} 2x + y = 10 \\ 5x - y = -3 \end{cases}

A

No

B

Only for the first equation

C

Yes

D

Cannot be determined

Correct Answer: C

Choice C is the correct answer. To verify if (1,8)(1, 8) is a solution, we substitute x=1x = 1 and y=8y = 8 into both equations.

First equation: 2x+y=102x + y = 102(1)+8=2+8=102(1) + 8 = 2 + 8 = 10 ✓ (True)

Second equation: 5xy=35x - y = -35(1)8=58=35(1) - 8 = 5 - 8 = -3 ✓ (True)

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

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

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

Choice B is incorrect because the point satisfies both equations, not just the first.

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