Solve y equals x2-4x plus 3 and y equals x-1 algebraically?

Answer 1

y = x2 - 4x + 3
y = x -1

Substitute the 2nd equation into the first

x -1 = x2 -4x + 3

Rearranging:

x2 -4x -x +3 +1 = 0
x2 - 5x +4 = 0

Solving this quadratic equation in x by factorising gives 2 values for x
x1 = 4
x2 = 1

Substituting these into the original equation for y (y=x-1) gives
y1 = 3
y2 = 0

So the 2 solutions to the equations are:
x1=4
y1=3

and

x2 = 1
y2 = 0