2
algebra

Solve the system using substitution: {x=4y2x+3y=55\begin{cases} x = 4y \\ 2x + 3y = 55 \end{cases}

A

(16,4)(16, 4)

B

(24,6)(24, 6)

C

(20,5)(20, 5)

D

(12,3)(12, 3)

Correct Answer: C

Choice C is the correct answer. Since x=4yx = 4y is already isolated, we can substitute it into the second equation.

Step 1: Substitute x=4yx = 4y into 2x+3y=552x + 3y = 55: 2(4y)+3y=552(4y) + 3y = 558y+3y=558y + 3y = 5511y=5511y = 55y=5y = 5

Step 2: Find xx using x=4yx = 4y: x=4(5)=20x = 4(5) = 20

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

Verification: 2(20)+3(5)=40+15=552(20) + 3(5) = 40 + 15 = 55

💡 Strategic Tip: When a variable is isolated, substitution is straightforward and efficient.

Choice A is incorrect because2(16)+3(4)=32+12=44 eq552(16) + 3(4) = 32 + 12 = 44 \ eq 55.

Choice B is incorrect because2(24)+3(6)=48+18=66 eq552(24) + 3(6) = 48 + 18 = 66 \ eq 55.

Choice D is incorrect because2(12)+3(3)=24+9=33 eq552(12) + 3(3) = 24 + 9 = 33 \ eq 55.