Class 9 Exam > Class 9 Questions > The linear equation 2x + 5y = 8 has:a)A uniqu...
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The linear equation 2x + 5y = 8 has:
- a)A unique solution
- b)Infinitely many solution
- c)No solution
- d)Two solution
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The linear equation 2x + 5y = 8 has:a)A unique solutionb)Infinitely ma...
Explanation:
The given linear equation is 2x + 5y = 8. To determine the number of solutions, we can convert this equation into slope-intercept form.
2x + 5y = 8
5y = -2x + 8
y = (-2/5)x + 8/5
Now we can see that the equation has a slope of -2/5 and a y-intercept of 8/5. This means that the equation represents a line in the coordinate plane.
Infinitely many solutions:
Since the equation represents a line, there are three possible scenarios for the number of solutions:
1. The line intersects the x-axis and y-axis at a single point. This would mean that the equation has a unique solution.
2. The line is parallel to the x-axis and does not intersect the y-axis. This would mean that the equation has no solution.
3. The line is neither parallel to the x-axis nor the y-axis. This would mean that the equation has infinitely many solutions.
In this case, the line has a slope of -2/5, so it is not parallel to the x-axis or the y-axis. Therefore, the equation has infinitely many solutions.
The given linear equation is 2x + 5y = 8. To determine the number of solutions, we can convert this equation into slope-intercept form.
2x + 5y = 8
5y = -2x + 8
y = (-2/5)x + 8/5
Now we can see that the equation has a slope of -2/5 and a y-intercept of 8/5. This means that the equation represents a line in the coordinate plane.
Infinitely many solutions:
Since the equation represents a line, there are three possible scenarios for the number of solutions:
1. The line intersects the x-axis and y-axis at a single point. This would mean that the equation has a unique solution.
2. The line is parallel to the x-axis and does not intersect the y-axis. This would mean that the equation has no solution.
3. The line is neither parallel to the x-axis nor the y-axis. This would mean that the equation has infinitely many solutions.
In this case, the line has a slope of -2/5, so it is not parallel to the x-axis or the y-axis. Therefore, the equation has infinitely many solutions.
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Community Answer
The linear equation 2x + 5y = 8 has:a)A unique solutionb)Infinitely ma...
Consider the equation ax+by=cax+by=c. Now we know that there is a number d=lcm(a,b)d=lcm(a,b). Let ad1=d and bd2=dad1=d and bd2=d. So, ad1−bd2=0ad1−bd2=0. Note that neither d1d1nor d2d2 is 00. ax+by+ad1−bd2=cax+by+ad1−bd2=c a(x+d1)+b(y−d2)=ca(x+d1)+b(y−d2)=c Thus, for every solution of this linear diophantine equation of two variables, there exists another unique solution. Hence, there is an infinite number of solutions to this equation.
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The linear equation 2x + 5y = 8 has:a)A unique solutionb)Infinitely many solutionc)No solutiond)Two solutionCorrect answer is option 'B'. Can you explain this answer?
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