Math Problem Statement
Solution
The given system of simultaneous equations is:
2a - 3b = 7 \tag{1} 3a + 2b = 4 \tag{2}
We can solve this using either substitution or elimination. I'll use elimination here for simplicity.
Step 1: Eliminate one variable
To eliminate , we'll multiply both equations by suitable coefficients to make the coefficients of equal in magnitude. Multiply (1) by 2 and (2) by 3:
4a - 6b = 14 \tag{3} 9a + 6b = 12 \tag{4}
Now add the two equations:
Step 2: Solve for
Substitute into either of the original equations. Using equation (1):
Final Answer:
The solution is:
Would you like further clarification or additional methods? Here are related questions you might consider:
- What are the advantages of solving by elimination compared to substitution?
- How would the solution change if the second equation were ?
- Can we verify the solution by substituting back into both equations?
- How can these techniques extend to three-variable systems?
- What are the practical applications of solving such equations?
Tip: Always verify your solution by substituting back into the original equations!
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Math Problem Analysis
Mathematical Concepts
Simultaneous Equations
Linear Equations
Elimination Method
Formulas
Linear equation format: ax + by = c
Theorems
Basic properties of equality
Suitable Grade Level
Grades 8-10
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