I have to identify the system of equations, if any for:
-2x-4=1,
12=-6x-3
no solution?
infinitely many solutions?
(0,-1)?
or
(-1,0)?
multiply the first by 3 and you have
-6x-12 = 3
12 = -6x-3
You can see that they are the same line. Plug any value of x into either equation, and you will get the same value for y.
To identify the system of equations, we need to solve each equation separately and then analyze the solutions.
Let's solve the first equation: -2x - 4 = 1.
To isolate the variable x, we can start by adding 4 to both sides of the equation:
-2x - 4 + 4 = 1 + 4,
-2x = 5.
Next, we divide both sides of the equation by -2 to solve for x:
-2x / -2 = 5 / -2,
x = -5/2.
Now, let's solve the second equation: 12 = -6x - 3.
To solve for x, we can start by adding 3 to both sides of the equation:
12 + 3 = -6x - 3 + 3,
15 = -6x.
Next, we divide both sides of the equation by -6 to find x:
15 / -6 = -6x / -6,
-5/2 = x.
Now, let's analyze the solutions:
Since the value of x in both equations is -5/2, we can say that the system of equations is consistent and has infinitely many solutions. The solution to the system of equations is x = -5/2.
The point (0, -1) and (-1, 0) are not solutions to the system of equations since neither of them satisfies both equations. Therefore, we can conclude that option "no solution" is incorrect, option "infinitely many solutions" is correct, and neither (0, -1) nor (-1, 0) are solutions to the system of equations.