Question

PLEASEE HELP ME 60 POINTS!!!

Answer 1

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.   $y =-4x - 5$

    $y = -4x + 1$

This gives

$-4x- 5 = -4x + 1$

which has no solutions.

 2. $-3x+y=7$

     $2x-4y=-8$

let us write them in y-intercept form

$y=3x+7$

$y=\frac{1}{2}x+2$

and equate them

$y=3x+7=\frac{1}{2}x+2$

this gives $x=-2$ and

$y=-3(-2)+7 = 1$

This equation has solutions.

3. $3x-y=4$

 $6x-2y =8$

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

$2(3x-y=4)\rightarrow (6x-2y=8)$

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