6
algebra

Solve the system: {y=3x2x+y=14\begin{cases} y = 3x - 2 \\ x + y = 14 \end{cases}

A

(5,13)(5, 13)

B

(3,7)(3, 7)

C

(4,10)(4, 10)

D

(6,8)(6, 8)

Correct Answer: C

Choice C is the correct answer. We use substitution since y=3x2y = 3x - 2 is already isolated.

Step 1: Substitute y=3x2y = 3x - 2 into x+y=14x + y = 14: x+(3x2)=14x + (3x - 2) = 144x2=144x - 2 = 144x=164x = 16x=4x = 4

Step 2: Find yy using y=3x2y = 3x - 2: y=3(4)2=122=10y = 3(4) - 2 = 12 - 2 = 10

Solution: (4,10)(4, 10)

Verification: 4+10=144 + 10 = 14

💡 Strategic Tip: When y is isolated, substitute directly into the other equation.

Choice A is incorrect because5+13=18 eq145 + 13 = 18 \ eq 14.

Choice B is incorrect because3+7=10 eq143 + 7 = 10 \ eq 14.

Choice D is incorrect because6+8=146 + 8 = 14 ✓, but 8 eq3(6)2=168 \ eq 3(6) - 2 = 16.