Determine the number of solutions to the system of linear equations
Y equals X +5
Y equals negative X +5
The given system of linear equations is:
Y = X + 5
Y = -X + 5
By setting the two equations equal to each other, we get:
X + 5 = -X + 5
Adding X to both sides:
2X + 5 = 5
Subtracting 5 from both sides:
2X = 0
Dividing by 2:
X = 0
Now, substitute X = 0 into one of the equations to find Y:
Y = 0 + 5
Y = 5
Therefore, the system of linear equations has only one solution, X = 0 and Y = 5.