The solution of given system equation can be calculated by using linear equation of two variable.
The correct option is [tex](3,\dfrac{1}{2})[/tex].
Given:
The given system equation is,
[tex]x+2y=4[/tex]
[tex]2x-2y=5[/tex]
The linear equation of two variables defines as an equation where a, b and r are real numbers where a and b both are not equal to 0.
[tex]ax+by=r[/tex]
Write the general linear equation of two variables.
[tex]a_1x+b_1y=r_1\\ a_2x+b_2y=r_2[/tex]
Comparing the above 4 equations.
[tex]a_1=1, b_1=2, r_1=4\\ a_2=2, b_2=-2,r_2=5[/tex]
Calculate the ratio of [tex]a_1[/tex] and [tex]a_2[/tex], [tex]b_1[/tex] and [tex]b_2[/tex].
[tex]\dfrac{a_1}{a_2}=\dfrac{1}{2}\\ \dfrac{b_1}{b_2}=\dfrac{2}{-2}=-1[/tex]
From the above calculation, [tex]\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}[/tex] the system of the equation has a unique solution.
Now, add the given equation,
[tex]3x=9\\ x=3[/tex]
Substitute the value of [tex]x[/tex] in above equation.
[tex]3+2y=4\\ y=\dfrac{1}{2}[/tex]
Thus, the correct option is [tex](3,\dfrac{1}{2})[/tex].
Learn more about linear equations here:
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