what is the solution to the system of equations?\ny = \\frac{1}{3}x - 10\n2x + y = 4\n(-8, 6)\n(-6, 16)\n(6…
what is the solution to the system of equations?\ny = \\frac{1}{3}x - 10\n2x + y = 4\n(-8, 6)\n(-6, 16)\n(6, -8)\n(16, -6)
Answer
Answer:
C. $(6, - 8)$
Explanation:
Step1: Substitute $y$ into second - equation
Substitute $y=\frac{1}{3}x - 10$ into $2x + y=4$. We get $2x+(\frac{1}{3}x - 10)=4$.
Step2: Simplify the equation
Combine like - terms: $2x+\frac{1}{3}x-10 = 4$. Then $\left(2+\frac{1}{3}\right)x=4 + 10$. $\frac{6 + 1}{3}x=14$, so $\frac{7}{3}x=14$.
Step3: Solve for $x$
Multiply both sides by $\frac{3}{7}$: $x=14\times\frac{3}{7}=6$.
Step4: Solve for $y$
Substitute $x = 6$ into $y=\frac{1}{3}x - 10$. Then $y=\frac{1}{3}\times6-10=2 - 10=-8$. So the solution is $(6,-8)$.