Math Problem Statement
Solution
The system of linear equations given in the image is:
To solve this by elimination, we first substitute the second equation into the first equation to eliminate .
Step 1: Substitute into :
Step 2: Simplify the equation:
Step 3: Solve for :
Step 4: Substitute back into the second equation to find :
Thus, the solution to the system of equations is and .
Solution set:
Would you like further details on elimination, or do you have any other questions?
Here are 5 questions to expand on this topic:
- What are other methods for solving a system of linear equations?
- How can substitution be used more generally to solve systems of equations?
- Can the graph of this system help visualize the solution?
- What does it mean geometrically when two lines intersect at one point?
- How would the solution change if the system had no solution or infinite solutions?
Tip: Always double-check your substitution to avoid simple mistakes in solving systems of equations!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
System of Equations
Elimination Method
Formulas
y = -x + 3
2x + y = 10
Theorems
Elimination Method
Substitution Method
Suitable Grade Level
Grades 8-10
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