Question

Without plotting the graphs, find the point of intersection of the lines 2x + 5y = 13 and 4x $-$ 9y = 7

Answer 1

The point of intersection of the lines 2x + 5y = 13 and 4x $-$ 9y = 7 will be the solution of
2x + 5y = 13 ...(1)
and
4x $-$ 9y = 7 ...(2)
Multiplying equation (1) by 2, we get:
4x + 10y = 26 ...(3)
Subtracting (3) from (2), we get:
4x $-$ 9y = 7
4x + 10y = 26
$-$ $-$ $-$
----------------------------
$-$ 19y = $-$19
$\Rightarrow y=\frac{-19}{-19}=1$
Substituting the value of y in equation (1), we get:

$$\begin{gathered} 2x+5\times 1=13 \\ \Rightarrow 2x+5=13 \\ \Rightarrow 2x=8 \\ \Rightarrow x=4 \end{gathered}$$
i.e., x = 4 and y = 1 is the solution of the given equations.
∴ (4, 1) is the point of intersection.