5
algebra

Solve using your preferred method: {3x+2y=18x4y=8\begin{cases} 3x + 2y = 18 \\ x - 4y = -8 \end{cases}

A

(3,4.5)(3, 4.5)

B

(4,3)(4, 3)

C

(2,6)(2, 6)

D

(5,1.5)(5, 1.5)

Correct Answer: B

Choice B is the correct answer. I'll use substitution. From second equation: x=4y8x = 4y - 8.

Step 1: Substitute into first equation: 3(4y8)+2y=183(4y - 8) + 2y = 1812y24+2y=1812y - 24 + 2y = 1814y=4214y = 42y=3y = 3

Step 2: Find xx: x=4(3)8=128=4x = 4(3) - 8 = 12 - 8 = 4

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

Verification: 3(4)+2(3)=183(4) + 2(3) = 18 ✓ and 44(3)=84 - 4(3) = -8

💡 Strategic Tip: With coefficient 1 on x in second equation, substitution is efficient.

Choice A is incorrect because3(3)+2(4.5)=183(3) + 2(4.5) = 18 ✓, but 34(4.5)=15 eq83 - 4(4.5) = -15 \ eq -8.

Choice C is incorrect because3(2)+2(6)=183(2) + 2(6) = 18 ✓, but 24(6)=22 eq82 - 4(6) = -22 \ eq -8.

Choice D is incorrect because3(5)+2(1.5)=183(5) + 2(1.5) = 18 ✓, but 54(1.5)=1 eq85 - 4(1.5) = -1 \ eq -8.