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Find 4 solutions for the linear equation:- 2x-3(y-2)=1?
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Find 4 solutions for the linear equation:- 2x-3(y-2)=1?
To find solutions for the linear equation \( 2x - 3(y - 2) = 1 \), we begin by simplifying and rearranging it.
Step 1: Rearranging the Equation
Rearranging gives us:
\[
2x - 3y + 6 = 1
\]
This simplifies to:
\[
2x - 3y = -5
\]
Step 2: Finding Solutions
We can express \( y \) in terms of \( x \):
\[
3y = 2x + 5 \implies y = \frac{2}{3}x + \frac{5}{3}
\]
This form allows us to choose different values for \( x \) to find corresponding values of \( y \).
Step 3: Choosing Values for \( x \)
Here are four potential solutions:
Conclusion
The four solutions for the equation \( 2x - 3(y - 2) = 1 \) are:
- \( (0, \frac{5}{3}) \)
- \( (3, \frac{11}{3}) \)
- \( (6, \frac{17}{3}) \)
- \( (-3, -\frac{1}{3}) \)
These solutions illustrate the relationship between \( x \) and \( y \) in the given linear equation.
Step 1: Rearranging the Equation
Rearranging gives us:
\[
2x - 3y + 6 = 1
\]
This simplifies to:
\[
2x - 3y = -5
\]
Step 2: Finding Solutions
We can express \( y \) in terms of \( x \):
\[
3y = 2x + 5 \implies y = \frac{2}{3}x + \frac{5}{3}
\]
This form allows us to choose different values for \( x \) to find corresponding values of \( y \).
Step 3: Choosing Values for \( x \)
Here are four potential solutions:
- Solution 1: Let \( x = 0 \)
Then, \( y = \frac{2}{3}(0) + \frac{5}{3} = \frac{5}{3} \)
So, the solution is \( (0, \frac{5}{3}) \). - Solution 2: Let \( x = 3 \)
Then, \( y = \frac{2}{3}(3) + \frac{5}{3} = 2 + \frac{5}{3} = \frac{11}{3} \)
So, the solution is \( (3, \frac{11}{3}) \). - Solution 3: Let \( x = 6 \)
Then, \( y = \frac{2}{3}(6) + \frac{5}{3} = 4 + \frac{5}{3} = \frac{17}{3} \)
So, the solution is \( (6, \frac{17}{3}) \). - Solution 4: Let \( x = -3 \)
Then, \( y = \frac{2}{3}(-3) + \frac{5}{3} = -2 + \frac{5}{3} = -\frac{1}{3} \)
So, the solution is \( (-3, -\frac{1}{3}) \).
Conclusion
The four solutions for the equation \( 2x - 3(y - 2) = 1 \) are:
- \( (0, \frac{5}{3}) \)
- \( (3, \frac{11}{3}) \)
- \( (6, \frac{17}{3}) \)
- \( (-3, -\frac{1}{3}) \)
These solutions illustrate the relationship between \( x \) and \( y \) in the given linear equation.
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Find 4 solutions for the linear equation:- 2x-3(y-2)=1?
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Find 4 solutions for the linear equation:- 2x-3(y-2)=1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find 4 solutions for the linear equation:- 2x-3(y-2)=1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find 4 solutions for the linear equation:- 2x-3(y-2)=1?.
Find 4 solutions for the linear equation:- 2x-3(y-2)=1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find 4 solutions for the linear equation:- 2x-3(y-2)=1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find 4 solutions for the linear equation:- 2x-3(y-2)=1?.
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