Math Problem Statement
For the two linear functions, find the point of intersection:
x=y+2 2x−3y=−1
Solution
To find the point of intersection of the two linear functions, we need to solve the system of equations formed by them:
Step 1: Substitute the expression for from the first equation into the second equation.
Since , substitute this into the second equation:
Step 2: Simplify and solve for .
Distribute the 2:
Combine like terms:
Subtract 4 from both sides:
Multiply both sides by -1:
Step 3: Substitute back into the first equation to find .
Using the first equation :
Step 4: Write the solution.
The point of intersection is .
Final Answer
The two lines intersect at the point .
Would you like more details or have any questions?
Here are some related questions:
- What is the graphical interpretation of the point of intersection?
- How would you verify the solution by substituting the values back into the original equations?
- How can you solve the system of equations using the elimination method?
- What happens if the two lines are parallel?
- Can we find the intersection of two linear functions if one or both are vertical lines?
Tip: When solving systems of linear equations, substituting one equation into another is a common method called the substitution method. This technique is particularly useful when one equation is already solved for one variable.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Substitution Method
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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