-x+2y=-2
x-2y=2
the system has no solution
the system has a unique solution:
the system has infinitely many solutions. they must satisfy the following equation: y=
the answer is the system has infinitely many solutions. i just don't understand how to get the equation y=?
equation 1 2 y = x - 2
equation 2 2 y = x - 2
or both are y = (1/2) x - 1
They are both the same line. ANY old x and y that fits one fits the other.
To determine the equation for y in a system of linear equations, we need to solve the system of equations simultaneously. Let's solve the system you provided step-by-step:
1. Let's rearrange the first equation, -x + 2y = -2, to isolate x.
-x + 2y = -2
x = 2y - 2
2. Now, substitute this expression for x in the second equation.
x - 2y = 2
(2y - 2) - 2y = 2
2y - 2 - 2y = 2
-2 = 2
3. This equation, -2 = 2, is not true. It represents a contradiction.
Based on this contradiction, we know the original system of equations has no solution. Therefore, the answer is that the system has no solution.
To determine the value of "y" in the equation y=, we need to solve the given system of equations:
-x + 2y = -2 ...(1)
x - 2y = 2 ...(2)
We can solve this system of equations using the method of elimination. By adding equations (1) and (2) together, we can eliminate the variable "x":
(-x + 2y) + (x - 2y) = (-2) + (2)
-2y = 0
y = 0
Now, we have found the value of "y" to be 0. So, to express the infinitely many solutions, we can rewrite the equation y= as y = 0.
Therefore, the system of equations has infinitely many solutions, and any solution to the system must satisfy the equation y = 0.