1
algebra

Solve using substitution: {2x+y=11x3y=8\begin{cases} 2x + y = 11 \\ x - 3y = 8 \end{cases}

A

(5,1)(5, 1)

B

(4,3)(4, 3)

C

(6,1)(6, -1)

D

(3,5)(3, 5)

Correct Answer: A

Choice A is the correct answer. First, we need to i- 2x+y=2(5)+1=112x + y = 2(5) + 1 = 11

  • x3y=?x - 3y = ?53(1)=25 - 3(1) = 2

Step 1: Isolate xx in the second equation: x=2+3yx = 2 + 3y

Step 2: Substitute into the first equation: 2(2+3y)+y=112(2 + 3y) + y = 114+6y+y=114 + 6y + y = 114+7y=114 + 7y = 117y=77y = 7y=1y = 1

Step 3: Find xx: x=2+3(1)=5x = 2 + 3(1) = 5

Solution: (5,1)(5, 1)

Verification: 2(5)+1=112(5) + 1 = 11 ✓ and 53(1)=25 - 3(1) = 2

💡 Strategic Tip: When neither variable is isolated, choose the variable with coefficient 1 for easier algebra.

Choice B is incorrect because2(4)+3=112(4) + 3 = 11 ✓, but 43(3)=5 eq24 - 3(3) = -5 \ eq 2.

Choice C is incorrect because2(6)+(1)=112(6) + (-1) = 11 ✓, but 63(1)=9 eq26 - 3(-1) = 9 \ eq 2.

Choice D is incorrect because2(3)+5=112(3) + 5 = 11 ✓, but 33(5)=12 eq23 - 3(5) = -12 \ eq 2.