4
algebra

Solve: {x+y=93x2y=7\begin{cases} x + y = 9 \\ 3x - 2y = 7 \end{cases}

A

(6,3)(6, 3)

B

(4,5)(4, 5)

C

(7,2)(7, 2)

D

(5,4)(5, 4)

Correct Answer: D

Choice D is the correct answer. Multiply first by 2 and add to second.

Step 1: Multiply first by 2: 2x+2y=182x + 2y = 18

Step 2: Add to second: (2x+2y)+(3x2y)=18+7(2x + 2y) + (3x - 2y) = 18 + 75x=255x = 25x=5x = 5

Step 3: Substitute: 5+y=9y=45 + y = 9 \Rightarrow y = 4

Solution: (5,4)(5, 4)

Verification: 3(5)2(4)=158=73(5) - 2(4) = 15 - 8 = 7

💡 Strategic Tip: Multiplying by 2 creates +2y+2y to cancel 2y-2y.

Choice A is incorrect because3(6)2(3)=12 eq73(6) - 2(3) = 12 \ eq 7.

Choice B is incorrect because3(4)2(5)=2 eq73(4) - 2(5) = 2 \ eq 7.

Choice C is incorrect because3(7)2(2)=17 eq73(7) - 2(2) = 17 \ eq 7.