Question
Solve the following systems of equations:
${\text{x}}+\frac{\text{y}}{2}=4,$
$\frac{\text{x}}{3}+2\text{y}=5.$
${\text{x}}+\frac{\text{y}}{2}=4,$
$\frac{\text{x}}{3}+2\text{y}=5.$
✓
Answer
The given equations are,
${\text{x}}+\frac{\text{y}}{2}=4\ .....(\text{i})$
$\frac{\text{x}}{3}+2\text{y}=5\ ......(\text{ii})$
Multiply equation $(i)$ by $4$ and subtract equations $(i) - (ii)$, we get $4x + 2y = 16$
$\Rightarrow\text{x}=3$
Put the value of x in equation (i), we get
$3+\frac{\text{y}}{2}=4$
$\Rightarrow\frac{\text{y}}{2}=1$
$\Rightarrow\text{y}=2$
Hence the value of $x$ and $y$ are $x = 3$ and $y = 2.$
${\text{x}}+\frac{\text{y}}{2}=4\ .....(\text{i})$
$\frac{\text{x}}{3}+2\text{y}=5\ ......(\text{ii})$
Multiply equation $(i)$ by $4$ and subtract equations $(i) - (ii)$, we get $4x + 2y = 16$
$\Rightarrow\text{x}=3$
Put the value of x in equation (i), we get
$3+\frac{\text{y}}{2}=4$
$\Rightarrow\frac{\text{y}}{2}=1$
$\Rightarrow\text{y}=2$
Hence the value of $x$ and $y$ are $x = 3$ and $y = 2.$
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