### Example 1: Using point of intersection formula, find the point of intersection of two lines 2x + 4y + 2 = 0 and 2x + 3y + 5 = 0.

**Solution:**

Given straight line equations are:

2x + 4y + 2 = 0 and 2x + 3y + 5 = 0

Here,

\(a_1 = 2, b_1 = 4, c_1 = 2\)

\(a_2 = 2, b_2 = 3, c_2 = 5\)

Intersection point can be calculated using the point of intersection formula,

\begin{array}{l}

\mathrm{x}=\frac{b_{1} c_{2}-b_{2} c_{1}}{a_{1} b_{2}-a_{2} b_{1}} ; \mathrm{y}=\frac{a_{2} c_{1}-a_{1} c_{2}}{a_{1} b_{2}-a_{2} b_{1}} \\

(\mathrm{x}, \mathrm{y})=\left(\frac{4 \times 5-3 \times 2}{2 \times 3-2 \times 4}, \frac{2 \times 2-2 \times 5}{2 \times 3-2 \times 4}\right) \\

(\mathrm{x}, \mathrm{y})=\left(\frac{20-6}{6-8}, \frac{4-10}{6-8}\right) \\

(\mathrm{x}, \mathrm{y})=(-7,3)

\end{array}