Question

Solve the following pair of simultaneous equations:
$\frac{x}{3}+y=1.7$ and $\frac{11}{x+\frac{y}{3}}=10$ for all $[x+\frac{y}{3}\ne 0]$

• A. $x=2$ and $y=7$
• B. $x=0.9$ and $y=-2.5$
• C. $x=0$ and $y=-4$
• D. $x=0.6$ and $y=1.5$

Answer 1

The correct option is D $x=0.6$ and $y=1.5$

Given equations are,

$\frac{x}{3}+y=1.7$

$\Rightarrow x+3y=5.1$ ....(1)

and $\frac{11}{x+\frac{y}{3}}=10$

$\Rightarrow \frac{33}{3x+y}=10$

$\Rightarrow 30x+10y=33$ ....(2)

Multiply equation (1) by $30$, we get

$30x+90y=153$ ....(3)

Subtract equations (2) and (3),

$80y=120$

$\Rightarrow y=\frac{12}{8}=1.5$

Put this value in equation (1), we get

$x+3\left(1.5\right)=5.1$

$\Rightarrow x+4.5=5.1$

$\Rightarrow x=5.1-4.5=0.6$

Therefore, the solution is $x=0.6,y=1.5$.