The linear system have zero number of solutions.
What is System of equations ?
System of equations is a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
We have,
[tex]y=-\frac{1}{2}x +4[/tex] [tex].....(i)[/tex]
And [tex]x+2y=-8[/tex] [tex].....(ii)[/tex]
Now,
Rewrite the first equation,
[tex]y=-\frac{1}{2}x +4[/tex]
[tex]2y=-x+8[/tex]
[tex]2y+x=8[/tex] [tex].....(iii)[/tex]
So,
Now compare ratios of equation [tex](iii)[/tex] and [tex](ii)[/tex] and ,
i.e.
[tex]\frac{a_{1} }{a_{2} } ,\frac{b_{1} }{b_{2} } ,\frac{c_{1} }{c_{2} }[/tex]
So,
[tex]\frac{a_{1} }{a_{2} } =\frac{1}{1}=1[/tex],
[tex]\frac{b_{1} }{b_{2} } =\frac{2}{2}=1[/tex],
[tex]\frac{c_{1} }{c_{2} } =\frac{8}{-8}=-1[/tex],
From ratios it is clear that,
[tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]
This means that these equations are parallel and have no solution.
Hence, we can say that the linear system have zero number of solutions.
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