Question

Question 13
Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x – y = 1, how many such lines can we find?

Answer 1

Now, x+y = 2 $\Rightarrow$ y = 2 – x
if x = 0, then y = 2 and if x = 2, then y = 0
$\begin{array}{ccc}X& 0& 2\\ Y& 2& 0\\ Points& a& B\end{array}$
and 2x – y – 1 = 0 $\Rightarrow$ y = 2x – 1
if x = 0, then y = -1 , if x = $\frac{1}{2}$ , then y = 0 and if x = 1, then y = 1
$\begin{array}{cccc}X& 0& \frac{1}{2}& 1\\ Y& -1& 0& 1\\ Points& C& D& E\end{array}$

Plotting the points A (2,0), we get the straight line AB. Ploting the points c (0, - 1) and ($\frac{1}{2}$, 0), we get the straight line CD. The lines AB and CD intersect at E (1, 1). Hence, infinite lines can pass through the intersection point of linear equations x + y = 2 and 2x – y = 1 i.e., E (1,1) like as y = x, 2x + y = 3, x + 2y = 3 so on.