Question

$$\begin{gathered} 2x+5y=1, \\ 2x+3y=3. \end{gathered}$$

Answer 1

The given equations may be written as:
2x + 5y − 1 = 0 ...(i)
2x + 3y − 3 = 0 ...(ii)
Here, a₁ = 2, b₁ = 5, c₁ = −1, a₂ = 2, b₂ = 3 and c₂ = −3
By cross multiplication, we have:

∴ $\frac{x}{\left[5\times \left(-3\right)-3\times \left(-1\right)\right]}=\frac{y}{\left[\left(-1\right)\times 2-\left(-3\right)\times 2\right]}=\frac{1}{\left[2\times 3-2\times 5\right]}$
⇒ $\frac{x}{\left(-15+3\right)}=\frac{y}{\left(-2+6\right)}=\frac{z}{\left(6-10\right)}$
⇒ $\frac{x}{-12}=\frac{y}{4}=\frac{1}{-4}$
⇒ $x=\frac{-12}{-4}=3,y=\frac{4}{-4}=-1$
Hence, x = 3 and y = −1 is the required solution.