Math Problem Statement
find the coordoinates of the points of intersection of the line y + 2x + 11 and the curve xy = 12
Solution
To find the points of intersection of the line and the curve , we need to solve this system of equations.
Step 1: Rearrange the equation of the line
First, express from the equation of the line in terms of :
Step 2: Substitute into the equation of the curve
Now, substitute into the curve equation :
Step 3: Simplify and solve for
Expanding the equation: Rearrange the terms:
Step 4: Solve the quadratic equation
Now solve the quadratic equation using the quadratic formula:
So, the two solutions for are:
Step 5: Find the corresponding values
For , substitute into :
For , substitute into :
Step 6: Conclusion
The points of intersection are:
Would you like more details or have any questions?
Here are some related questions:
- How do you solve quadratic equations by factoring?
- What are the general methods to solve systems of equations?
- How do you check the solutions of a system of equations?
- What is the importance of the quadratic formula?
- Can every system of equations be solved using substitution?
Tip: Always check your solutions by substituting them back into the original equations.
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Math Problem Analysis
Mathematical Concepts
Algebra
System of Equations
Quadratic Equations
Formulas
Equation of a line: y = mx + b
Quadratic equation formula: ax^2 + bx + c = 0
Theorems
Quadratic formula
Suitable Grade Level
Grades 9-11
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