Question

Determine, graphically whether the system of equations $x-2y=2$, $4x-2y=5$ is consistent or inconsistent.

Answer 1

The above image shows the line represented in the coordinate plane.

We know that, Slope of $1^{st}$ line =$\frac{-1}{-2}=\frac{1}{2}$

Slope of $2^{nd}$ line =$\frac{-4}{-2}=2$

Both lines have different slopes

$\Rightarrow$They will intersect at a point and hence system have consistent solutions