Refer to the graph below. The system of equations consists of y = 4x - 3 and y = -2x + 9. Determine the coordinates of the intersection point, which is the solution to the system. The solution is _______.
Answer & Analysis
Analysis
Question Analysis
This question evaluates the student's ability to find the solution to a system of linear equations by identifying the intersection point on a graph.
Key Concept Explanation
The solution to a system of equations is the point where the graphs of the equations intersect. For linear systems, this can be a single point, no points (parallel lines), or infinitely many points (identical lines).
Step-by-step Solution
1. Graph the equation (a line with slope 4 and y-intercept -3).
2. Graph the equation (a line with slope -2 and y-intercept 9).
3. Identify the intersection point of the two lines, which is .
4. Verify the solution by substituting and into both equations:
For
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