2
algebra

Solve the system using substitution: {y=x+73x2y=8\begin{cases} y = x + 7 \\ 3x - 2y = -8 \end{cases}

A

(4,11)(4, 11)

B

(6,13)(6, 13)

C

(2,9)(2, 9)

D

(5,12)(5, 12)

Correct Answer: B

Choice B is the correct answer. Since y=x+7y = x + 7 is already isolated, we can substitute it into the second equation.

Step 1: Substitute y=x+7y = x + 7 into 3x2y=83x - 2y = -8: 3x2(x+7)=83x - 2(x + 7) = -83x2x14=83x - 2x - 14 = -8x14=8x - 14 = -8x=6x = 6

Step 2: Find yy using y=x+7y = x + 7: y=6+7=13y = 6 + 7 = 13

Solution: (6,13)(6, 13)

Verification: 3(6)2(13)=1826=83(6) - 2(13) = 18 - 26 = -8

💡 Strategic Tip: When one equation is already solved for a variable, substitution is the most efficient method.

Choice A is incorrect because3(4)2(11)=1222=10 eq83(4) - 2(11) = 12 - 22 = -10 \ eq -8.

Choice C is incorrect because3(2)2(9)=618=12 eq83(2) - 2(9) = 6 - 18 = -12 \ eq -8.

Choice D is incorrect because3(5)2(12)=1524=9 eq83(5) - 2(12) = 15 - 24 = -9 \ eq -8.