The solution to which system of equations has a negative x-value?
x=y−1
−x+y=−1
x=−1−2y
3x+4y=−3
y=x+5
3x+y=25
y=x+2
4x+y=2
To find the solution with a negative x-value, we need to first solve each system of equations for x and y, and then check if the x-value is negative.
1. x = y - 1
-x + y = -1
Substitute x into the second equation:
-(y - 1) + y = -1
-y + 1 + y = -1
1 = -1
This system of equations has no solution.
2. x = -1 - 2y
3x + 4y = -3
Substitute x into the second equation:
3(-1 - 2y) + 4y = -3
-3 - 6y + 4y = -3
-2y = 0
y = 0
x = -1 - 2(0)
x = -1
The solution to this system of equations is x = -1, which is negative.
3. y = x + 5
3x + y = 25
Substitute y into the second equation:
3x + (x + 5) = 25
4x + 5 = 25
4x = 20
x = 5
y = 5 + 5
y = 10
The solution to this system of equations is x = 5, which is positive.
4. y = x + 2
4x + y = 2
Substitute y into the second equation:
4x + (x + 2) = 2
5x + 2 = 2
5x = 0
x = 0
y = 0 + 2
y = 2
The solution to this system of equations is x = 0, which is not negative.
Therefore, the solution to the system of equations with a negative x-value is x = -1, y = 0.