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A science test which is worth 100 points consist of 24 Questions each question is worth either 3 points or 5 points if X is the number of 3 point questions and why is the number number of 5 point the system shown represents this situation x+y=24 3x+5y =100 what does dissolution of the system indicate about the questions on the test 



Answer :

Answer:

There are 10 3-point questions, and 14 5-point questions.

Step-by-step explanation:

System of Equations

When presented with two or more equations, all with the same set of variables, the values of each of them can be calculated by using either the

  • substitution method

(rearrange and plug an equation into another)

  • elimination method

(multiply an equation by a factor and subtract it from another equation to eliminate a variable).

[tex]\hrulefill[/tex]

Solving the Problem

We're given the equations

                                        [tex]x+y=24[/tex]

and

                                     [tex]3x+5y=100[/tex].

Substitution Method

We can rearrange the first equation to have x in terms of y and plug it into the second equation!

                                          [tex]x=24-y[/tex]

                                 [tex]3(24-y)+5y=100[/tex]

                                   [tex]72-3y+5y=100[/tex]

                                       [tex]72+2y=100[/tex]

                                             [tex]2y=28[/tex]

                                    [tex]\boxed{y=14} \rightarrow \boxed{x = 10}[/tex]

[tex]\dotfill[/tex]

Elimination Method (Quicker)

We can multiply the first equation by 3 (or 5) and subtract it from the second.

                            [tex]3(x+y=24)\rightarrow 3x+3y=72[/tex]

                                        [tex]\:\:\:\:\:\:3x + 5y &= 100 \\-(3x + 3y &= 72) \\[/tex]

                                                     [tex]2y=28[/tex]

                                         [tex]\boxed{y=14}\rightarrow\boxed{x=10}[/tex]

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