Determine the number of solutions to the system of linear equations

Question

Y equals X +5
Y equals negative X +5

Answer 1

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.