Mathematics

Question

HELP PLEASE
How many solutions exist for the system of equations below?

3x+y=18
3x+y=16

none
one
two
infinite

2 Answer

  • The answer is none, as the same equation is equal to different numerical values
  • Answer:

    The correct option is 1.

    Step-by-step explanation:

    The system of equation is

    [tex]3x+y=18[/tex]

    [tex]3x+y=16[/tex]

    A system of equation has two equation [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex].

    1. If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex], then system of equations has no solution.

    2. If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex], then system of equations has infinite solution.

    3. If [tex]\frac{a_1}{a_2}neq \frac{b_1}{b_2}[/tex], then system of equation has one solution.

    In the given system of equations,

    [tex]a_1=3,b_1=1,c_1=8, a_2=3,b_2=1, c_2=16[/tex]

    [tex]\frac{a_1}{a_2}=\frac{3}{3}=1[/tex]

    [tex]\frac{b_1}{b_2}=\frac{1}{1}=1[/tex]

    [tex]\frac{c_1}{c_2}=\frac{18}{16}=\frac{9}{8}[/tex]

    Since [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex], therefore the system of equation has no solution.

    The correct option is 1.

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