8
algebra

Solve: {5x+3y=292xy=5\begin{cases} 5x + 3y = 29 \\ 2x - y = 5 \end{cases}

A

(7,2)(7, -2)

B

(4,3)(4, 3)

C

(5,43)(5, \frac{4}{3})

D

(3,143)(3, \frac{14}{3})

Correct Answer: B

Choice B is the correct answer. Multiply second equation by 3 and add to first.

Step 1: Multiply second by 3: 6x3y=156x - 3y = 15

Step 2: Add to first: (5x+3y)+(6x3y)=29+15(5x + 3y) + (6x - 3y) = 29 + 1511x=4411x = 44x=4x = 4

Step 3: Substitute: 2(4)y=5y=32(4) - y = 5 \Rightarrow y = 3

Solution: (4,3)(4, 3)

Verification: 5(4)+3(3)=295(4) + 3(3) = 29 ✓ and 2(4)3=52(4) - 3 = 5

💡 Strategic Tip: Multiplying by 3 creates 3y-3y to cancel +3y+3y.

Choice A is incorrect because2(7)(2)=16 eq52(7) - (-2) = 16 \ eq 5.

Choice C is incorrect because5(5)+3(43)=295(5) + 3(\frac{4}{3}) = 29 ✓, but 2(5)43 eq52(5) - \frac{4}{3} \ eq 5.

Choice D is incorrect because5(3)+3(143)=295(3) + 3(\frac{14}{3}) = 29 ✓, but 2(3)143 eq52(3) - \frac{14}{3} \ eq 5.