Question

Use the substitution method to solve the following system of linear equations:

x + y = 6
x = –y + 2

Answer 1

x+y = 6
-y+2+y = 6 ... replace x with -y+2
(-y+y) + 2 = 6
(-1y+1y) + 2 = 6
(-1+1)y + 2 = 6
0y + 2 = 6
0+2 = 6
2 = 6 ... this equation is false

Since the last equation is false, this means that no matter what we pick for x and y, there is no solution. This system is inconsistent. The two lines are parallel (they never intersect to form a solution)