9
algebra

Solve using your preferred method: {x+2y=112x+3y=18\begin{cases} x + 2y = 11 \\ 2x + 3y = 18 \end{cases}

A

(5,3)(5, 3)

B

(3,4)(3, 4)

C

(4,3.5)(4, 3.5)

D

(6,2.5)(6, 2.5)

Correct Answer: B

Choice B is the correct answer. I'll use elimination by multiplying first equation by 2.

Step 1: Multiply first by 2: 2x+4y=222x + 4y = 22

Step 2: Subtract second equation: (2x+4y)(2x+3y)=2218(2x + 4y) - (2x + 3y) = 22 - 18y=4y = 4

Step 3: Substitute: x+2(4)=11x=3x + 2(4) = 11 \Rightarrow x = 3

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

Verification: 2(3)+3(4)=182(3) + 3(4) = 18

💡 Strategic Tip: Multiplying first by 2 creates matching 2x2x terms for easy elimination.

Choice A is incorrect because2(5)+3(3)=19 eq182(5) + 3(3) = 19 \ eq 18.

Choice C is incorrect because2(4)+3(3.5)=18.5 eq182(4) + 3(3.5) = 18.5 \ eq 18.

Choice D is incorrect because2(6)+3(2.5)=19.5 eq182(6) + 3(2.5) = 19.5 \ eq 18.