Question

The pair of equations x = 0 and x = 5 has (a) no solution (b) unique/one solution (c) two solutions (d) infinitely many solutions

Answer 1

The pair of equations x = 0 and x = 5 has no solution

Given : The pair of equation x = 0 and x = 5

To find : The pair of equations has

(a) no solution

(b) unique/one solution

(c) two solutions

(d) infinitely many solutions

Solution :

Step 1 of 2 :

Write down the given pair of equations

Here the given pair of equations are

x = 0 and x = 5

Step 2 of 2 :

Find number of solutions

Now x = 0 represents the y axis

x = 5 represents the equation of the line parallel to y axis at a distance 5 unit from origin

So x = 0 and x = 5 represents two parallel lines

We know that two parallel lines never intersect

Also it is obvious that for the given two pair of equations the point of intersection is the solution of the equations

Since x = 0 and x = 5 never intersect

So there exists no solution

Hence the correct option is (a) no solution

Graph : Graph is referred to the attachment . In the graph green line represents x = 0 and red line denote x = 5

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