Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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 

Sagot :

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]

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.