Question

how many solutions of these there equations x minus 4 Y - 6 equal to zero and 3 x minus 12 Y - 18 is equal to zero will have​

Answer 1

Step-by-step explanation:

First of all, you need to understand what a solution is.

In the context of the given question, it simply means the point of intersection of the two given curves (in this case, the curves are x=0 and x=5).

The number of solution simply means the number of such points.

There are two ways (known to me) in which you can approach the solution (the answer indeed, not the one mentioned above!).

First method (graphical and recommended):

You draw the curves in a graph paper and simply count the number of points of intersection (that is the answer you need).

Observe that the given equations are linear and and so the graph is a straight line

Equations of the form ax + by + c = 0 represents a straight line.

You can see that you just keep x coordinate as c( =0 in first case and c= 5 in latter) as there is no condition on the y coordinate, it can take any value. So, on graph paper you put a dot on every point with x-coordinate as c and you cover every y -coordinate. You end up getting infinite number of dots with given conditions satisfied. You guessed it right! that is a line. So you draw it yourself, and you will see that the two lines are parallel and will not intersect each other at any point, so the number of solutions is zero.

Second method ( analytical ):

Let the solution exist and let the solution be (x, y) =(a,b).

As it satisfies both the given equations,

From the first given equation x=0→a=0

From the second given equation x=5→a=5

As a cannot be simultaneously both 0 and 5, our assumption that a solution exist is wrong and hence no solution for given system of equation exist. Hence the number of solutions for the given pair of equations is zero.

I hope that you got the answer and with the help of some knowledge you just got, you will be able to solve any related question…

Answer 2

There are infinitely many solutions for given equations

Given:

The equations are

x minus 4y - 6 equal to zero and

3 x minus 12y - 18 is equal to zero  

To find:

From the data, the equations are

=>  x- 4y - 6 = 0 ---- (1)

=> 3x - 12y - 18 = 0 --- (2)

Equation (2) can be converted as follows

=> 3x - 12y - 18 = 0

Divided the equation by 3

=>  x - 4y - 6 = 0 ----- (3)

From (2) and (3)

Both equations represent the same line or two Coincident lines

Since two coincident lines will have infinitely many solutions

The solutions of equations (1) and (2) are infinite

Therefore,

There are infinitely many solutions for given equations.

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