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Which one of the following options is true for the equation y = 3x+5y?
- a)It has a unique solution
- b)It has only two solutions
- c)It has infinitely many solutions
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Which one of the following options is true for the equation y = 3x+5y?...
- A linear equation in two variables has infinitely many solutions, corresponding to all the points on the line.
- Therefore, the correct answer is:
- C: It has infinitely many solutions.
- Therefore, the correct answer is:
- C: It has infinitely many solutions.
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Community Answer
Which one of the following options is true for the equation y = 3x+5y?...
Understanding the Equation
The given equation is y = 3x + 5y. To determine the number of solutions it has, we can rearrange it.
Rearranging the Equation
1. Start with the original equation:
- y = 3x + 5y
2. Subtract 5y from both sides:
- y - 5y = 3x
- -4y = 3x
3. Now, express y in terms of x:
- y = -3/4 x
Analyzing the Equation
This final form, y = -3/4 x, is a linear equation in slope-intercept form (y = mx + b), where:
- m (slope) = -3/4
- b (y-intercept) = 0
Determining the Solutions
- Unique Solution: A unique solution would occur if the equation represented a single line that intersects the axes at one point. However, this equation represents a straight line.
- Infinitely Many Solutions: Since it is a linear equation, every point (x, y) on this line is a solution to the equation. Thus, there are infinitely many solutions.
Conclusion
- The correct answer is option C: it has infinitely many solutions. This is because any value of x will yield a corresponding value of y along the line defined by the equation y = -3/4 x.
The given equation is y = 3x + 5y. To determine the number of solutions it has, we can rearrange it.
Rearranging the Equation
1. Start with the original equation:
- y = 3x + 5y
2. Subtract 5y from both sides:
- y - 5y = 3x
- -4y = 3x
3. Now, express y in terms of x:
- y = -3/4 x
Analyzing the Equation
This final form, y = -3/4 x, is a linear equation in slope-intercept form (y = mx + b), where:
- m (slope) = -3/4
- b (y-intercept) = 0
Determining the Solutions
- Unique Solution: A unique solution would occur if the equation represented a single line that intersects the axes at one point. However, this equation represents a straight line.
- Infinitely Many Solutions: Since it is a linear equation, every point (x, y) on this line is a solution to the equation. Thus, there are infinitely many solutions.
Conclusion
- The correct answer is option C: it has infinitely many solutions. This is because any value of x will yield a corresponding value of y along the line defined by the equation y = -3/4 x.
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