Problem 46
Question
Use a graphing utility to graph each equation. $$7 x^{2}+8 x y+y^{2}-1=0$$
Step-by-Step Solution
Verified Answer
By correctly inputting the equation into graphing utility and generating the graph, the solutions of the equation can be visually demonstrated as points where the graph crosses the x and y axes.
1Step 1: Input the Equation into Graphing Utility
The equation given is a quadratic equation with x and y variables. To graph it, the equation \(7x^{2}+8xy+y^{2}-1=0\) needs to be input into the graphing tool. Most graphing utilities will have an input field where this equation can be directly typed in.
2Step 2: Graph the Equation
Once the equation is input correctly, the next step is to run or 'graph' the equation. The graphing tool will make what's called a 'scatter plot', showing all the points (x, y) that satisfy the equation.
3Step 3: Interpret the Graph
The graph will visually represent all solutions to the equation. It might be a curve, parabola or any other shape depending on the given equation. The aim is to look where this curve or line crosses the x and y axis. Those points are the solutions to the equation.
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