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PLEASEE HELP ME 60 POINTS!!!

Match each system of linear equations with the correct number of solutions.

A. No Solution B. Infinitely many solutions C. One Solution

1. y = -4x-5 ------------> _________
y = -4x+1

2. -3x+y = 7 -----------> _________
2x-4y = -8

3. 3x-y = 4 ------------> _________
6x-2y = 8

Respuesta :

Poltergeist

Answer:

1. No Solution

2. One solution

3. Infinitely many solutions

Step-by-step explanation:

Let us try to solve each of the system of equations one by one.

1.   [tex]y =-4x - 5[/tex]

    [tex] y = -4x + 1[/tex]

This gives

[tex]-4x- 5 = -4x + 1 [/tex]

which has no solutions.

 2. [tex]-3x+y=7[/tex]

     [tex]2x-4y=-8[/tex]

let us write them in y-intercept form

[tex]y=3x+7[/tex]

[tex]y=\frac{1}{2}x+2 [/tex]

and equate them

[tex]y=3x+7=\frac{1}{2}x+2[/tex]

this gives [tex]x=-2[/tex] and

[tex]y=-3(-2)+7 = 1[/tex]

This equation has solutions.

3. [tex]3x-y=4[/tex]

 [tex]6x-2y =8[/tex]

Notice that the second equation is just the first equation multiplied by 2, or

[tex]2(3x-y=4)\rightarrow (6x-2y=8)[/tex]

so these are identical equations and therefore this system has infinitely many solutions.

Thus we have

1. No Solution

2. One solution

3. Infinitely many solutions

Answer:

1. no

2.Inf

3. one

Step-by-step explanation:

because