How to solve a linear system algebraically?

Question

how to I find out if these two lines intersect? 

y = -x + 5 
y = -x + 4

Answer 1

Substitution Method :

The system of equations are y = - x + 5 and y = - x + 4.

Step 1 : The equation 1 : y = - x + 5 is already solved for y.

Step 2 : Substitute - x + 5 for y in the equation 2 : y = - x + 4 to find the value of x.

(- x + 5) = - x + 4

Add x to each side.

- x + 5 + x = - x + 4 + x

5 = 4.

The variables are eliminated and we are left with a false statement regardless of the values of x and y. This tells you that the system has no solution.