Which of the following uses the substitution method to solve linear-quadratic system y=x2−4x+8, y=3x−4?(
To use the substitution method to solve the linear-quadratic system, we need to solve one equation for one variable and substitute it into the other equation.
From the given system:
y = x^2 - 4x + 8 (Equation 1)
y = 3x - 4 (Equation 2)
Since Equation 2 is already solved for y, we can substitute it into Equation 1:
3x - 4 = x^2 - 4x + 8
Now we have a quadratic equation:
x^2 - 4x + 8 - 3x + 4 = 0
x^2 - 7x + 12 = 0
We can factor this quadratice equation:
(x - 3)(x - 4) = 0
Setting each factor equal to zero:
x - 3 = 0 -> x = 3
x - 4 = 0 -> x = 4
Therefore, the solution to the linear-quadratic system is x = 3 and x = 4.