Question
Solve for x and y:
$\frac{\text{x}}{2}-\frac{\text{y}}2{}=6,$
$\frac{\text{x}}{7}+\frac{\text{y}}{3}=5$
$\frac{\text{x}}{2}-\frac{\text{y}}2{}=6,$
$\frac{\text{x}}{7}+\frac{\text{y}}{3}=5$
✓
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
$\frac{\text{x}}{7}+\frac{\text{y}}{3}=5\ \dots(\text{ii})$
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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