Math Problem Statement
Solution
The problem in your image involves finding the point where two lines intersect, with equations given as:
Step 1: Set the equations equal to each other.
To find the intersection, we set because at the point of intersection, both -values are the same:
Step 2: Solve for .
Rearrange the terms to solve for :
Step 3: Substitute into either equation to find .
Substitute into either or :
- Using :
Thus, the point of intersection is .
Step 4: Graph the lines.
Now, we will graph the two lines using their equations:
- For , this is a line with slope and y-intercept .
- For , this is a line with slope and y-intercept .
Both lines will intersect at the point .
Would you like more details or help with graphing these lines?
Follow-up Questions:
- Can you solve for the intersection of any two lines by setting the equations equal to each other?
- What is the geometric significance of the slopes of the two lines in this problem?
- How does changing the slope or intercept affect the intersection point?
- Can you verify the solution graphically by plotting both lines on the grid?
- How would you find the intersection if the lines were parallel or identical?
Tip: The intersection point of two lines represents the solution to the system of equations, as the point satisfies both equations simultaneously.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Graphing
Formulas
y1 = 2 - x
y2 = 3x - 2
Theorems
Intersection of two lines
Solving systems by substitution
Suitable Grade Level
Grades 7-10