6
algebra

Solve the system: {y=2x3x+y=25\begin{cases} y = 2x \\ 3x + y = 25 \end{cases}

A

(4,8)(4, 8)

B

(6,12)(6, 12)

C

(3,6)(3, 6)

D

(5,10)(5, 10)

Correct Answer: D

Choice D is the correct answer. We use substitution since y=2xy = 2x is already isolated.

Step 1: Substitute y=2xy = 2x into 3x+y=253x + y = 25: 3x+(2x)=253x + (2x) = 255x=255x = 25x=5x = 5

Step 2: Find yy using y=2xy = 2x: y=2(5)=10y = 2(5) = 10

Solution: (5,10)(5, 10)

Verification: 3(5)+10=15+10=253(5) + 10 = 15 + 10 = 25

💡 Strategic Tip: Substitution works beautifully when one variable is already isolated.

Choice A is incorrect because3(4)+8=12+8=20 eq253(4) + 8 = 12 + 8 = 20 \ eq 25.

Choice B is incorrect because3(6)+12=18+12=30 eq253(6) + 12 = 18 + 12 = 30 \ eq 25.

Choice C is incorrect because3(3)+6=9+6=15 eq253(3) + 6 = 9 + 6 = 15 \ eq 25.