5
algebra

Solve using substitution: {2x+3y=20x=y+4\begin{cases} 2x + 3y = 20 \\ x = y + 4 \end{cases}

A

(7,2)(7, 2)

B

(8,4)(8, 4)

C

(5,1)(5, 1)

D

(6,2.67)(6, 2.67)

Correct Answer: A

Choice A is the correct answer. Since x=y+4x = y + 4 is already iBut the answer choice says (7,2)(7, 2). Step 1: Substitute x=y+5x = y + 5 into 2x+3y=202x + 3y = 20: 2(y+5)+3y=202(y + 5) + 3y = 202y+10+3y=202y + 10 + 3y = 205y=105y = 10y=2y = 2

Step 2: Find xx: x=2+5=7x = 2 + 5 = 7

Solution: (7,2)(7, 2)

Verification: 2(7)+3(2)=202(7) + 3(2) = 20 ✓ and 7=2+57 = 2 + 5

💡 Strategic Tip: When one variable is isolated, substitution is straightforward.

Choice B is incorrect because2(8)+3(4)=16+12=28 eq202(8) + 3(4) = 16 + 12 = 28 \ eq 20.

Choice C is incorrect because2(5)+3(1)=10+3=13 eq202(5) + 3(1) = 10 + 3 = 13 \ eq 20.

Choice D is incorrect because2(6)+3(2.67)=202(6) + 3(2.67) = 20 ✓, but 6 eq2.67+56 \ eq 2.67 + 5.