6
algebra

Solve the system: {y=4x2x+y=30\begin{cases} y = 4x \\ 2x + y = 30 \end{cases}

A

(6,24)(6, 24)

B

(4,16)(4, 16)

C

(5,20)(5, 20)

D

(3,12)(3, 12)

Correct Answer: C

Choice C is the correct answer. We use substitution since y=4xy = 4x is already isolated.

Step 1: Substitute y=4xy = 4x into 2x+y=302x + y = 30: 2x+(4x)=302x + (4x) = 306x=306x = 30x=5x = 5

Step 2: Find yy using y=4xy = 4x: y=4(5)=20y = 4(5) = 20

Solution: (5,20)(5, 20)

Verification: 2(5)+20=10+20=302(5) + 20 = 10 + 20 = 30

💡 Strategic Tip: Substitution works best when one equation is already solved for a variable.

Choice A is incorrect because2(6)+24=12+24=36 eq302(6) + 24 = 12 + 24 = 36 \ eq 30.

Choice B is incorrect because2(4)+16=8+16=24 eq302(4) + 16 = 8 + 16 = 24 \ eq 30.

Choice D is incorrect because2(3)+12=6+12=18 eq302(3) + 12 = 6 + 12 = 18 \ eq 30.