2
algebra

Solve the system using substitution: {x=5y2x+y=33\begin{cases} x = 5y \\ 2x + y = 33 \end{cases}

A

(10,2)(10, 2)

B

(20,4)(20, 4)

C

(15,3)(15, 3)

D

(25,5)(25, 5)

Correct Answer: C

Choice C is the correct answer. Since x=5yx = 5y is already isolated, we can directly substitute it into the second equation.

Step 1: Substitute x=5yx = 5y into 2x+y=332x + y = 33: 2(5y)+y=332(5y) + y = 3310y+y=3310y + y = 3311y=3311y = 33y=3y = 3

Step 2: Find xx using x=5yx = 5y: x=5(3)=15x = 5(3) = 15

Solution: (15,3)(15, 3)

Verification: 2(15)+3=30+3=332(15) + 3 = 30 + 3 = 33

💡 Strategic Tip: When a variable is already isolated, substitution is the most efficient method.

Choice A is incorrect because2(10)+2=20+2=22 eq332(10) + 2 = 20 + 2 = 22 \ eq 33.

Choice B is incorrect because2(20)+4=40+4=44 eq332(20) + 4 = 40 + 4 = 44 \ eq 33.

Choice D is incorrect because2(25)+5=50+5=55 eq332(25) + 5 = 50 + 5 = 55 \ eq 33.