A catering company is setting up for a wedding they expect 150 people to attend they can provide tables that seat 6 people and large tables that seats 10 people Is the point (20,5) a solution to the equation 6x+10y=150 explain the point (20,5) means in context

We have been given that a catering company is expecting 150 people to attend the wedding. There are two types of tables, ones which can fit 6 people and ones which can fit 10 people.

If there are x tables which can fit 6 people and there are y tables which can fit 10 people, we can express the total number of people that can fit on all available tables as: [tex]6x+10y[/tex].

Since there are total 150 people expected in the wedding, the equation can be framed as: [tex]6x+10y=150[/tex].

Let us check if the point (20,5) is a solution of the equation.

[tex]6*20+10*5=150[/tex]

[tex]120+50=150[/tex]

[tex]170=150[/tex]

Since we get a false statement, therefore, (20,5) is NOT a solution of the equation [tex]6x+10y=150[/tex].

The point (20,5) implies that there are 20 small tables and 5 large tables.