Question

Question 1
Graphically, the pair of equations
6x – 3y + 10 = 0
x – y + 9 = 0
Represents two lines which are
(A) intersecting at exactly one point.
(B) intersecting at exactly two points.
(C) coincident.
(D) parallel.

Answer 1

The first equation is
$6x–3y+10=0$
$\Rightarrow 2x-y+\frac{10}{3}=0$
$y=2x+\frac{10}{3}$

$\begin{array}{ccc}x& 0& -\frac{5}{3}\\ y& \frac{10}{3}& 0\\ Points& A& B\end{array}Andtablefor2x-y+9=0\begin{array}{ccc}x& 0& -\frac{9}{2}\\ Y=2x+9& 9& 0\\ Points& C& D\end{array}$

Hence, the pair of equations represents two parallel lines