Math Problem Statement
what is the intersection of y=3-x and y=2x
Solution
We are given two equations:
y = 3 - x \tag{1} y = 2x \tag{2}
To find the point of intersection, we need to solve this system of equations by setting the right-hand sides equal to each other (since both equal ):
Step 1: Solve for
Add to both sides:
Now, divide by 3:
Step 2: Solve for
Substitute into either equation. Let's use equation :
Final solution:
The point of intersection is:
Thus, the lines intersect at the point .
Would you like to explore this concept further?
Here are 8 related questions for further exploration:
- What happens if you change the equations to and ?
- How would you find the intersection point using substitution or elimination methods?
- Can these equations be solved graphically? What does the graph look like?
- How would the intersection change if one equation was ?
- What is the geometric interpretation of this solution?
- What if you had a system of three linear equations—how would you find their intersection?
- How would you find the intersection of a linear equation and a quadratic equation?
- Can you solve this system using matrix methods?
Tip: Plotting the equations on a graph can give a visual representation of where the lines intersect.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Intersection of Lines
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9
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