Question

$$\begin{gathered} 3x+2y+25=0, \\ 2x+y+10=0. \end{gathered}$$

Answer 1

The given equations are:
3x + 2y + 25 = 0 ...(i)
2x + y + 10 = 0 ...(ii)
Here, a₁ = 3, b₁ = 2 , c₁ = 25, a₂ = 2, b₂ = 1 and c₂ = 10
By cross multiplication, we have:

∴ $\frac{x}{\left[2\times 10-25\times 1\right]}=\frac{y}{\left[25\times 2-10\times 3\right]}=\frac{1}{\left[3\times 1-2\times 2\right]}$
⇒ $\frac{x}{\left(20-25\right)}=\frac{y}{\left(50-30\right)}=\frac{1}{\left(3-4\right)}$
⇒ $\frac{x}{\left(-5\right)}=\frac{y}{20}=\frac{1}{\left(-1\right)}$
⇒ $x=\frac{-5}{-1}=5,y=\frac{20}{\left(-1\right)}=-20$
Hence, x = 5 and y = −20 is the required solution.