Question

How many solutions does the system of equations have `y= 5x + 2; y = 5x - \frac { 4} { 9}`?

Answer 1

The lines are parallel, so there is no intersection, therefore no solution.

Explanation:

Both of these equation are for straight lines because they are in the form `y=mx+c`

However, they both have the same slope. `m = 5`, which means that these lines are parallel.

Parallel lines never intersect, so there is no solution for these two equations.

Answer 2

0 solution

Explanation:

Both are linear equations, with the formula `y=mx+c`. Linear equations can only have either 0, 1 or `oo` numbers of solutions.

In this case, 1 solution is not possible as the values of `x` is equivalent.

In this case, `oo` numbers of solutions is also not possible as the values of `x` and `c` are not equal.

Hence, leaving us with 0 number of solutions, proving the two linear equations to be parallel.