2x + 4y = 12\n y = \\frac{1}{4}x - 3\n what is the solution to the system of equations?\n (-1, 8)\n (8…
2x + 4y = 12\n y = \\frac{1}{4}x - 3\n what is the solution to the system of equations?\n (-1, 8)\n (8, -1)\n (5, \\frac{1}{2})\n (\\frac{1}{2}, 5)
Answer
Explanation:
Step1: Substitute y into first - equation
Substitute $y=\frac{1}{4}x - 3$ into $2x + 4y=12$. We get $2x+4(\frac{1}{4}x - 3)=12$.
Step2: Expand and simplify
Expand the left - hand side: $2x + 4\times\frac{1}{4}x-4\times3 = 12$, which simplifies to $2x+x - 12=12$. Combine like terms: $3x-12 = 12$.
Step3: Solve for x
Add 12 to both sides: $3x=12 + 12$, so $3x=24$. Divide both sides by 3: $x = 8$.
Step4: Solve for y
Substitute $x = 8$ into $y=\frac{1}{4}x - 3$. Then $y=\frac{1}{4}\times8-3=2 - 3=-1$.
Answer:
B. $(8, - 1)$