The System of solutions will give infinite number of solutions.
[tex]\dfrac{1}{2}x+5y=6[/tex]
[tex]3x +30y =36[/tex]
[tex]\dfrac{1}{2}x+5y=6[/tex]
solving for x,
[tex]\dfrac{1}{2}x+5y=6\\\\\dfrac{x+10y}{2}=6\\\\x+10y = 12\\\\x=12-10y[/tex]
[tex]3x +30y =36[/tex]
Substitute the value of x in equation 2,
[tex]3(12-10y) +30y =36\\36-30y+30y = 36\\36-36 = 30y-30y\\0=0[/tex]
As we can see both the equations are returning 0 on both sides of the equations, therefore, the system of solution will give infinite number of solutions.
Also, to verify we can plot the graph of the equations. the graph will give us two coinciding lines.
Hence, the System of solutions will give infinite number of solutions.
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