Question

Solve the following pair of equations by cross multiplication rule

$5x+3y=35,2x+4y=28$

Then

• A. $x=4$, $y=5$
• B. $x=5$, $y=4$
• C. $x=6$, $y=3$
• D. $x=3$, $y=6$

Answer 1

The correct option is A $x=4$, $y=5$

The equations are
$\Rightarrow 5x+3y-35=0$
$\Rightarrow 2x+4y-28=0$
By cross multiplication
$\Rightarrow \frac{x}{[3\times (-28)-4\times (-35)]}=\frac{y}{[-35\times 2-(-28)\times 5]}=\frac{1}{[5\times 4-2\times 3]}$

$\Rightarrow \frac{x}{-84+140}=\frac{y}{-70+140}=\frac{1}{20-6}$

$\Rightarrow \frac{x}{56}=\frac{y}{70}=\frac{1}{14}$

$\Rightarrow \frac{x}{56}=\frac{1}{14}\Rightarrow 14x=56\Rightarrow x=4$

$\Rightarrow \frac{y}{70}=\frac{1}{14}\Rightarrow 14y=70\Rightarrow y=5$

$\Rightarrow x=4,y=5$