Question

Select the expression you will get for x and y if you solve the following equations using the cross multiplication method.
$\sqrt{3}x=2$
$\frac{x}{3}=7-\frac{y}{5}$

• A. $x=\frac{(0\times -7)-(-2\times \frac{1}{5})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})},y=\frac{(0\times -7)-(-2\times \frac{1}{5})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})}$
• B. $x=\frac{(0\times -7)-(-2\times \frac{1}{5})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})},y=\frac{(-2\times \frac{1}{3})-(-7\times \sqrt{3})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})}$
• C. $x=\frac{(-2\times \frac{1}{3})-(-7\times \sqrt{3})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})}y=\frac{(0\times -7)-(-2\times \frac{1}{5})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})}$
• D. $x=\frac{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})}{(0\times -7)-(-2\times \frac{1}{5})},y=\frac{(-2\times \frac{1}{3})-(-7\times \sqrt{3})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})}$

Answer 1

The correct option is B $x=\frac{(0\times -7)-(-2\times \frac{1}{5})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})},y=\frac{(-2\times \frac{1}{3})-(-7\times \sqrt{3})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})}$

The given equations can be written in the general form as follows:
$\sqrt{3}x=2$
$\Rightarrow \sqrt{3}x-0.y-2=0$
$\frac{x}{3}=7-\frac{y}{5}$
$\Rightarrow \frac{x}{3}+\frac{y}{5}-7=0$
Using cross multiplication,

Thus, the solutions are:
$\frac{x}{(0\times 7)-(-2\times \frac{1}{5})}=\frac{1}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})};\frac{y}{(-2\times \frac{1}{3})-(-7\times \sqrt{3})}=\frac{1}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})}$
$\Rightarrow x=\frac{(0\times -7)-(-2\times \frac{1}{5})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})},y=\frac{(-2\times \frac{1}{3})-(-7\times \sqrt{3})}{(\sqrt{3}\times \frac{1}{5})-(0\times \frac{1}{3})}$