which graph shows a system of equations that solves -\\frac{2}{x - 1}=4, and the solution itself?
which graph shows a system of equations that solves -\\frac{2}{x - 1}=4, and the solution itself?
Answer
Answer:
First, rewrite the equation (-\frac{2}{x - 1}=4) as a system of equations. We can set (y =-\frac{2}{x - 1}) and (y = 4).
To solve the equation (-\frac{2}{x - 1}=4) for (x): [ \begin{align*} -\frac{2}{x - 1}&=4\
- 2&=4(x - 1)\ -2&=4x-4\ 4x&=2\ x&=\frac{1}{2} \end{align*} ]
The system of equations (y =-\frac{2}{x - 1}) and (y = 4) will have a solution at the (x) - value where the graph of the rational function (y =-\frac{2}{x - 1}) intersects the horizontal line (y = 4). The solution of the equation (-\frac{2}{x - 1}=4) is (x=\frac{1}{2}).
The graph that shows the rational function (y =-\frac{2}{x - 1}) (a hyperbola with a vertical asymptote at (x = 1)) and the horizontal line (y = 4) intersecting at (x=\frac{1}{2}) is the correct one.
We need to find the graph with the horizontal line (y = 4) intersecting the hyperbola (y=-\frac{2}{x - 1}) at (x=\frac{1}{2}).
The second - graph shows the horizontal line (y = 4) and the hyperbola (y=-\frac{2}{x - 1}) and their intersection point represents the solution of the given equation.
Explanation:
Step1: Rewrite as system
Set (y =-\frac{2}{x - 1}) and (y = 4).
Step2: Solve for (x)
Cross - multiply (-\frac{2}{x - 1}=4) to get (-2 = 4(x - 1)).
Step3: Expand and isolate (x)
Expand to (-2=4x - 4), then (4x=2) and (x=\frac{1}{2}).
Step4: Identify graph
Look for graph with (y = 4) intersecting (y=-\frac{2}{x - 1}) at (x=\frac{1}{2}).