Solve the system by the method of your choice. Identify systems with no solutions and systems with infinitely many solutions, using set notation to express their solutions:
x + y = 3
-2 + y = -3
(0 ,-5)
(0 , 0)
(-2 ,-1)
(-2,-3)
x + y = 3 should be - 3
If -2+y = -3, then y = -1
If also x+y = -3, then
x-1 = -3 and x = -2
(-2,-1) is the answer
thanks that's what I had I just wasn't sure if -2 + y = -3 (-2,-1) if I multipied -2(-2, -1)
To solve the system of equations:
1. Start with the given equations:
Equation 1: x + y = 3
Equation 2: -2 + y = -3
2. From Equation 2, we can rewrite it as:
y = -3 + 2
Simplifying, we get:
y = -1
3. Now, substitute the value of y = -1 into Equation 1:
x + (-1) = 3
Simplifying, we get:
x - 1 = 3
Add 1 to both sides:
x = 4
4. Therefore, the solution to the system of equations is x = 4 and y = -1.
Checking the answers with the given options:
- (0, -5): Substitute x = 0 and y = -5 into both equations:
Equation 1: 0 + (-5) = 3 (False)
Equation 2: -2 + (-5) = -3 (True)
- (0, 0): Substitute x = 0 and y = 0 into both equations:
Equation 1: 0 + 0 = 3 (False)
Equation 2: -2 + 0 = -3 (False)
- (-2, -1): Substitute x = -2 and y = -1 into both equations:
Equation 1: -2 + (-1) = 3 (False)
Equation 2: -2 + (-1) = -3 (True)
- (-2, -3): Substitute x = -2 and y = -3 into both equations:
Equation 1: -2 + (-3) = 3 (False)
Equation 2: -2 + (-3) = -3 (True)
Out of the given options, only (-2, -1) and (-2, -3) satisfy both equations simultaneously. Therefore, the system has infinitely many solutions.
Using set notation to express the solutions:
The set notation for the solutions to the system is {(-2, -1), (-2, -3)}.