Question

$$\begin{gathered} 7x-2y=3, \\ 22x-3y=16. \end{gathered}$$

Answer 1

The given equations may be written as:
7x − 2y − 3 = 0 ...(i)
$22x-3y-16=0$ ...(ii)
Here, a₁ = 7, b₁ = −2 , c₁ = −3, a₂ = 22, b₂ = $-3$ and c₂ = −16
By cross multiplication, we have:

∴ $\frac{x}{\left[\left(-2\right)\times \left(-16\right)-\left(-{\displaystyle 3}\right)\times \left(-3\right)\right]}=\frac{y}{\left[\left(-3\right)\times 22-\left(-16\right)\times 7\right]}=\frac{1}{\left[7\times \left({\displaystyle -3}\right)-22\times \left(-2\right)\right]}$
⇒ $\frac{x}{\left(32-9\right)}=\frac{y}{\left(-66+112\right)}=\frac{1}{\left(-21+44\right)}$
⇒ $\frac{x}{\left({\displaystyle 23}\right)}=\frac{y}{46}=\frac{1}{\left({\displaystyle 23}\right)}$
⇒ $x=\frac{{\displaystyle 23}}{{\displaystyle 23}}=1,y=\frac{46}{23}=2$
Hence, x = 1 and y = 2 is the required solution.