5
algebra

Solve using substitution: {2x3y=11x=2y+5\begin{cases} 2x - 3y = 11 \\ x = 2y + 5 \end{cases}

A

(9,2)(9, 2)

B

(7,1)(7, 1)

C

(11,3)(11, 3)

D

(5,0)(5, 0)

Correct Answer: B

Choice B is the correct answer. Since x=2y+5x = 2y + 5 is already isolated, substitute.

Step 1: Substitute into first: 2(2y+5)3y=112(2y + 5) - 3y = 114y+103y=114y + 10 - 3y = 11y=1y = 1

Step 2: Find x: x=2(1)+5=7x = 2(1) + 5 = 7

Solution: (7,1)(7, 1)

Verification: 2(7)3(1)=143=112(7) - 3(1) = 14 - 3 = 11

💡 Strategic Tip: When x is isolated, substitute directly.

Choice A is incorrect because2(9)3(2)=12 eq112(9) - 3(2) = 12 \ eq 11.

Choice C is incorrect because2(11)3(3)=13 eq112(11) - 3(3) = 13 \ eq 11.

Choice D is incorrect because2(5)3(0)=10 eq112(5) - 3(0) = 10 \ eq 11.