solve the system bysubstitution. y=×^2-2×+1 y=2×+1

Answer 1

To solve the system of equations by substitution, we can substitute one equation into the other equation and solve for the variable.

Substituting the expression for y from the second equation into the first equation, we have:

2x + 1 = x^2 - 2x + 1

Rearranging this equation, we get:

x^2 - 4x = 0

Factoring out an x, we have:

x(x - 4) = 0

This equation is satisfied when x = 0 or x - 4 = 0.

For x = 0, substituting this value back into the second equation, we get:

y = 2(0) + 1 = 1

Therefore, one solution to the system of equations is (0, 1).

For x - 4 = 0, we have:

x = 4

Substituting this value back into the second equation, we get:

y = 2(4) + 1 = 9

Therefore, another solution to the system of equations is (4, 9).

Hence, the system of equations has two solutions: (0, 1) and (4, 9).