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Solve 2x + 3y = 11
3x - 2y = 9
using elimination method only?
3x - 2y = 9
using elimination method only?
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Solve 2x + 3y = 11 3x - 2y = 9 using elimination method only?
Solving a System of Equations using Elimination Method
Step 1: Multiply the Equations
- Multiply the first equation by 2 and the second equation by 3 to make the coefficients of either x or y the same in both equations.
- This gives us:
4x + 6y = 22
9x - 6y = 27
Step 2: Add the Equations
- Add the two new equations together to eliminate the variable y.
- 4x + 6y + 9x - 6y = 22 + 27
- This simplifies to: 13x = 49
Step 3: Solve for x
- Divide both sides by 13 to find the value of x.
- x = 49/13
- x = 3
Step 4: Substitute x back into an original equation
- Use x = 3 in the first original equation to solve for y.
- 2(3) + 3y = 11
- 6 + 3y = 11
- 3y = 5
- y = 5/3
Step 5: Verify the Solution
- Substitute x = 3 and y = 5/3 into the second original equation to ensure it holds true.
- 3(3) - 2(5/3) = 9
- 9 - 10/3 = 9
- 27/3 - 10/3 = 9
- 17/3 = 9
- The solution is verified.
Therefore, the solution to the system of equations 2x + 3y = 11 and 3x - 2y = 9 is x = 3 and y = 5/3.
Step 1: Multiply the Equations
- Multiply the first equation by 2 and the second equation by 3 to make the coefficients of either x or y the same in both equations.
- This gives us:
4x + 6y = 22
9x - 6y = 27
Step 2: Add the Equations
- Add the two new equations together to eliminate the variable y.
- 4x + 6y + 9x - 6y = 22 + 27
- This simplifies to: 13x = 49
Step 3: Solve for x
- Divide both sides by 13 to find the value of x.
- x = 49/13
- x = 3
Step 4: Substitute x back into an original equation
- Use x = 3 in the first original equation to solve for y.
- 2(3) + 3y = 11
- 6 + 3y = 11
- 3y = 5
- y = 5/3
Step 5: Verify the Solution
- Substitute x = 3 and y = 5/3 into the second original equation to ensure it holds true.
- 3(3) - 2(5/3) = 9
- 9 - 10/3 = 9
- 27/3 - 10/3 = 9
- 17/3 = 9
- The solution is verified.
Therefore, the solution to the system of equations 2x + 3y = 11 and 3x - 2y = 9 is x = 3 and y = 5/3.
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Solve 2x + 3y = 11 3x - 2y = 9 using elimination method only?
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Solve 2x + 3y = 11 3x - 2y = 9 using elimination method only? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Solve 2x + 3y = 11 3x - 2y = 9 using elimination method only? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve 2x + 3y = 11 3x - 2y = 9 using elimination method only?.
Solve 2x + 3y = 11 3x - 2y = 9 using elimination method only? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Solve 2x + 3y = 11 3x - 2y = 9 using elimination method only? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve 2x + 3y = 11 3x - 2y = 9 using elimination method only?.
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