2
algebra

Solve the system using substitution: {y=3xx+y=16\begin{cases} y = 3x \\ x + y = 16 \end{cases}

A

(5,11)(5, 11)

B

(3,9)(3, 9)

C

(4,12)(4, 12)

D

(6,10)(6, 10)

Correct Answer: C

Choice C is the correct answer. Since y=3xy = 3x is already isolated, we can directly substitute it into the second equation.

Step 1: Substitute y=3xy = 3x into x+y=16x + y = 16: x+(3x)=16x + (3x) = 164x=164x = 16x=4x = 4

Step 2: Find yy using y=3xy = 3x: y=3(4)=12y = 3(4) = 12

Solution: (4,12)(4, 12)

Verification: 4+12=164 + 12 = 16 ✓ and 12=3(4)12 = 3(4)

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

Choice A is incorrect because5+11=165 + 11 = 16 ✓, but 11 eq3(5)=1511 \ eq 3(5) = 15.

Choice B is incorrect because3+9=12 eq163 + 9 = 12 \ eq 16.

Choice D is incorrect because6+10=166 + 10 = 16 ✓, but 10 eq3(6)=1810 \ eq 3(6) = 18.