Question

What is the solution to the system of equations below?

Answer 1

$\left\{\begin{array}{ccc}y=\frac{1}{2}x-4\\y=-2x-9\end{array}\right\Rightarrow\dfrac{1}{2}x-4=-2x-9\\\\\dfrac{1}{2}x-4=-2x-9\ \ \ |\cdot2\\\\x-8=-4x-18\ \ \ |+8\\\\x=-4x-10\ \ \ |+4x\\\\5x=-10\ \ \ |:5\\\\\boxed{x=-2}\\\text{substitute the value of x to the second equation}\\y=-2(-2)-9=4-9=-5\\\boxed{y=-5}\\\\\text{Answer:}\ x=-2;\ y=-5\to(-2;-5)$