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Question 3(Multiple Choice Worth 4 points)

(08.03)Solve the system of equations and choose the correct answer from the list of options.

2x + y = −4
y = 3x + 2

negative 6 over five comma negative 8 over 5
negative 8 over 5 comma negative 6 over 5
negative 5 over 6 comma negative 11 over 5
negative 11 over 5 comma negative 6 over 5

Respuesta :

apologiabiology
subsitution

y=3x+2
subsitute (3x+2) for y in other equation

2x+y=-4
2x+(3x+2)=-4
2x+3x+2=-4
5x+2=-4
minus 2 both sides
5x=-6
divide both sides by 5
[tex]x=\frac{-6}{5}[/tex]

subsitute back

[tex]y=3x+2[/tex]
[tex]y=3(\frac{-6}{5})+2[/tex]
[tex]y=\frac{-18}{5}+2[/tex]
[tex]y=\frac{-18}{5}+\frac{10}{5}[/tex]
[tex]y=\frac{-18+10}{5}[/tex]
[tex]y=\frac{-8}{5}[/tex]


[tex]x=\frac{-6}{5}[/tex]
[tex]y=\frac{-8}{5}[/tex]

(x,y)
[tex](\frac{-6}{5},\frac{-8}{5})[/tex]



the solution is [tex](\frac{-6}{5},\frac{-8}{5})[/tex]
that is the first option

Answer:

The solution of the system of equations is:

                          negative 6 over 5 comma negative 8 over 5.

Step-by-step explanation:

We are given a system of linear equations as:

                          2x + y = −4 ------------(1)

                         y = 3x + 2------------(2)

Now we solve the system of equations using the substitution method.

i.e. we substitute the value of y in terms of x from equation (2) in equation (1) and find the value of x and y.

i.e.

2x+3x+2= -4

i.e.  5x+2= -4

i.e.  5x= -6

i.e.  x= -6/5

Similarly, on putting this value of x in equation (2) we obtain:

y= -8/5

               Hence, the solution is:

                           [tex](-\dfrac{6}{5},-\dfrac{8}{5})[/tex]

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