Solve for x and y: x 2 - y 2 =6, x 7 + y 3 =5 - Vidyadip

Question

Solve for $x$ and $y:$
$\frac{\text{x}}{2}-\frac{\text{y}}2{}=6,$
$\frac{\text{x}}{7}+\frac{\text{y}}{3}=5$

✓

Answer

$\frac{\text{x}}{2}-\frac{\text{y}}2{}=6\ \dots(\text{i})$
$\frac{\text{x}}{7}+\frac{\text{y}}{3}=5\ \dots(\text{ii})$
Multiply $(ii)$ by $\frac{1}{3}$ and add it to $(i).$
$\frac{\text{x}}{21}+\frac{\text{y}}9{}=\frac{5}{3}$ and $\frac{\text{x}}{2}-\frac{\text{y}}{9}=6$
$\Rightarrow\frac{\text{x}}{21}+\frac{\text{x}}{2}=\frac{5}{3}+6$
$\Rightarrow\frac{23\text{x}}{42}=\frac{23}{3}$
$\Rightarrow\text{x}=14$
Substituting $x = 14$ in $(ii),$ we get $y = 9$
So, $x = 14$ and $y = 9$

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