Question

How do you solve the system of equations: `6x - 2y = 5` and `3x - y = 10`?

Answer 1

There is no solution to these systems of equations.

Explanation:

To solve the system of equations: `6x−2y=5` and `3x−y=10`, let us find the value of `y` in terms of `x` using second equation.

It is obvious that `3x=y+10` or `y=3x-10`

Now putting `y=3x-10` in first equation i.e. `6x−2y=5`, we get

`6x−2(3x-10)=5`

or `6x−6x-20=5` or

or `-20=5`, which is not possible

Hence there is no solution to these system of equations. In fact, if we draw the equations on a graph, these represent two parallel lines (who do not meet and hence here is no solution).

In case, if in any other case, you get `0=0`, this means that for every `x` there will be a corresponding `y` and hence infinite solutions. In such case, drawing equations of lines on a graph will result in two coincident (i.e. only one line) lines, all points on which will be a solution, hence infinite solutions.