Question
Solve the following systems of equations:
${\text{x}}+2{\text{y}}=\frac{3}{2},$
$2\text{x}+\text{y}=\frac{3}{2}.$
${\text{x}}+2{\text{y}}=\frac{3}{2},$
$2\text{x}+\text{y}=\frac{3}{2}.$
✓
Answer
The given system of equations is,
${\text{x}}+2{\text{y}}=\frac{3}{2}\ .....(\text{i})$
$2\text{x}+\text{y}=\frac{3}{2}\ .......(\text{ii})$
Let us eliminate y from the given equations. The co-efficients of y in the given equations are 2 and 1 respectively. The L.C.M of 2 and 1 is. so, we make the co-efficients of y equal to 2 in the equations.
Multiplying (i) by 1 and (ii) by 2, we get
${\text{x}}+2{\text{y}}=\frac{3}{2}\ .....(\text{iii})$
$4\text{x}+2\text{y}=3\ .....(\text{iv})$
Subtracting (iii) from (iv), we get
$4\text{x}-\text{x}+2\text{y}-2\text{y}=3-\frac{3}{2}$
$\Rightarrow3\text{x}=\frac{6-3}{2}$
$\Rightarrow3\text{x}=\frac{3}{2}$
$\Rightarrow\text{x}=\frac{3}{2\times3}$
$\Rightarrow\text{x}=\frac{1}{2}$
Putting $\text{x}=\frac{1}{2},$ in equation (iv), we get
$4\times\frac{1}{2}+2\text{y}=3$
$\Rightarrow2+2\text{y}=3$
$\Rightarrow2\text{y}=3-2$
$\Rightarrow\text{y}=\frac{1}{2}$
Hence, solution of the given of equation is $\text{x}=\frac{1}{2},\text{y}=\frac{1}{2}.$
${\text{x}}+2{\text{y}}=\frac{3}{2}\ .....(\text{i})$
$2\text{x}+\text{y}=\frac{3}{2}\ .......(\text{ii})$
Let us eliminate y from the given equations. The co-efficients of y in the given equations are 2 and 1 respectively. The L.C.M of 2 and 1 is. so, we make the co-efficients of y equal to 2 in the equations.
Multiplying (i) by 1 and (ii) by 2, we get
${\text{x}}+2{\text{y}}=\frac{3}{2}\ .....(\text{iii})$
$4\text{x}+2\text{y}=3\ .....(\text{iv})$
Subtracting (iii) from (iv), we get
$4\text{x}-\text{x}+2\text{y}-2\text{y}=3-\frac{3}{2}$
$\Rightarrow3\text{x}=\frac{6-3}{2}$
$\Rightarrow3\text{x}=\frac{3}{2}$
$\Rightarrow\text{x}=\frac{3}{2\times3}$
$\Rightarrow\text{x}=\frac{1}{2}$
Putting $\text{x}=\frac{1}{2},$ in equation (iv), we get
$4\times\frac{1}{2}+2\text{y}=3$
$\Rightarrow2+2\text{y}=3$
$\Rightarrow2\text{y}=3-2$
$\Rightarrow\text{y}=\frac{1}{2}$
Hence, solution of the given of equation is $\text{x}=\frac{1}{2},\text{y}=\frac{1}{2}.$
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