Set 15: Systems of Equations

Choice A is correct. Choice A is the correct answer. First, we need to i- $2x + y = 2(5) + 1 = 11$ ✓ - $x - 3 y = ?$ → $5- 3(1) = 2$ Step 1: Isolate $x$ in the second equation: $x = 2 + 3 y$ Step 2: Substitute into the first equation: 2(2 + 3 y) + y = 11$4+ 6 y + y = 114+ 7 y = 117y = 7$y = 1 Step 3: Find $x$: $x = 2 + 3(1) = 5$ Solution: $(5, 1)$ Verification: $2(5) + 1 = 11$ ✓ and $5- 3(1) = 2$ ✓ Strategic Tip: When neither variable is isolated, choose the variable with coefficient 1 for easier algebra. Choice B is incorrect because $2(4) + 3 = 11$ ✓, but $4- 3(3) = -5 \neq 2$. Choice C is incorrect because $2(6) + (-1) = 11$ ✓, but $6- 3(-1) = 9 \neq 2$. Choice D is incorrect because $2(3) + 5 = 11$ ✓, but $3- 3(5) = -12 \neq 2$.