4

Set 12: Systems of Equations

Explanation

Answer: C

Verify if (7,2)(7, 2) is the solution to: {5x−3y=292x+4y=22\begin{cases} 5x - 3y = 29 \\ 2x + 4y = 22 \end{cases}

A.

No, it only satisfies the first equation

B.

No, it satisfies neither equation

C.

Yes

✓ Correct
D.

No, it only satisfies the second equation

Detailed Explanation

Choice C is correct. Choice C is the correct answer. First equation: 5x−3y=295(7)−3(2)=35−6=295x - 3 y = 295(7) - 3(2) = 35 - 6 = 29 ✓ Second equation: 2x+4y=222(7)+4(2)=14+8=222x + 4 y = 222(7) + 4(2) = 14 + 8 = 22 ✓ Since (7,2)(7, 2) satisfies both equations, it is the Choice A is incorrect because the point satisfies both equations. Choice B is incorrect because the point does satisfy both equations. Choice D is incorrect because the point satisfies both, not just the second.

Key Steps:

•

The correct answer is Yes

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
B: Choice B is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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