Question

If a system of equations in two variables has a unique solution, then the lines on the graph are_________

Answer 1

Define a linear equation and understand its graphical representation

Linear equation in two variables: An equation of the form $ax+by+c=0$ is said to be a linear equation in two variables $x,y$. It is a linear equation as the exponents of both the variables are equal to $1$.

A linear equation in two variables represents a straight line in cartesian co-ordinates.

A system of linear equations in two variables is said to have a unique solution if and only if , the lines represented by the equations intersect at a single point.

Say two lines are given by $ax+by+c=0$ and $dx+ey+f=0$

These lines can intersect only when their slopes are unequal.

$\Rightarrow$ $\frac{-a}{b}\ne \frac{-d}{e}$

Hence , unique solution only exists when the graphs of the lines are intersecting.