please solve with steps thank you PlODiem Sel 4 ch 11 and 12

please solve with steps
thank you

PlODiem Sel 4 (ch 11 and 12) Quiz Barbara Roubik: Attempt 1 Question 2 (4 points) Solve the nonlinear system of equations shown below. Hint- Use substitution method by plugging (x 1) into the bottom equation in place of y @Me

Solution

Substituting y=x-1 in 2nd equation

x-1=x²-6x+9 => x²-6x-x+9+1=0 => x²-7x+10=0 => x²-5x-2x+10=0 => x(x-5) -2(x-5)=0 => (x-2)(x-5)=0

=> x-2=0 or x-5=0 => x=2 or x=5