The correct option is B.[tex](3,\frac{1}{2})[/tex]
Given equations,
[tex]x+2y=4.....(1)\\2x-2y=5.....(2)[/tex]
The standard form for linear equations in two variables is [tex]Ax+By=C[/tex].
On comparing equation 1 and equation 2 with the standard form we get,
[tex]a_{1}=1, b_{1}=2, c_{1}=4\\a_{2}=2, b_{2}=-2,c_{2}=5[/tex]
Here,
[tex]\frac{a_{1} }{a_{2} } =\frac{1}{2} \\[/tex] and [tex]\frac{b_{1} }{b_{2} } =\frac{2}{-2} =-1[/tex]
Since [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex], So the given system of equation has a unique solution.
Now Adding equation 1 and 2 we get,
[tex]3x=9\\x=3[/tex]
putting the value of x in equation 1 we get,
[tex]3+2y=4\\2y=1\\y=\frac{1}{2}[/tex].
Hence the required solution of equation is [tex](3,\frac{1}{2})[/tex]. the correct option is B.[tex](3,\frac{1}{2})[/tex]
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https://brainly.com/question/11897796
