The number of solutions of the two equations 4x-y=2 and 2x-8y+4=0 isa)Zerob)Onec)Twod)Infinitely manyCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Explanation:

To find the number of solutions of the given equations, we can start by analyzing the system of equations and determining the relationship between the two equations.

The given system of equations is:
1) 4x - y = 2
2) 2x - 8y + 4 = 0

Step 1: Simplify the equations
To make the equations easier to work with, we can rearrange them to isolate the variables on one side:

Equation 1: 4x - y = 2
Rearranging, we have:
y = 4x - 2

Equation 2: 2x - 8y + 4 = 0
Rearranging, we have:
2x - 8y = -4
Dividing by 2, we get:
x - 4y = -2

Step 2: Compare the equations
By comparing the two equations, we can see that they have the same slope (4) and different y-intercepts (-2 and -2). This indicates that the equations represent two parallel lines in the coordinate plane.

Step 3: Determine the number of solutions
Since the two equations represent parallel lines, they will never intersect. Therefore, there are no common points of intersection and no solutions to the system of equations.

Conclusion:
The number of solutions of the given system of equations is zero (option A).

Similar Defence Doubts

Let [x] denote the greatest integer function. What is the number of solutions of the equation x2 + 4x + [x] = 0 in the interval [0,2]?

Which of the following are correct in respect of the system of equations x + y + z =8, x -y +2z = 6 and 3x -y +5z = k?1. They have no solution, if k = 15.2. They have infinitely many solutions, if k = 20.3. They have unique solution, if k = 25Q. Select the correct answer using the code given below

The system of equations2x+ y – 3z = 53x – 2y + 2z = 5 and5x – 3y – z = 16

The equationsx + 2y+ 3z= 12x+ y+ 3z= 25x+ 5y+ 9z= 4

What is the number of distinct solutions of the equation z2 + |z| = 0(where z is a complex number)?

Top Courses for Defence

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams