Which of the following uses the substitution method to solve linear-quadratic system y=x2−4x+8 , y=3x−4 ?(1 point)
The linear-quadratic system is given as y = x^2 - 4x + 8 and y = 3x - 4.
To solve using the substitution method, we'll substitute the expression for y in terms of x from the second equation into the first equation.
Substituting 3x - 4 for y in the first equation, we get:
3x - 4 = x^2 - 4x + 8
Rearranging the equation, we have:
x^2 - 4x + 8 - 3x + 4 = 0
Combining like terms, we have:
x^2 - 7x + 12 = 0
Now we can factor the quadratic equation:
(x - 3)(x - 4) = 0
Setting each factor equal to zero, we get:
x - 3 = 0 or x - 4 = 0
Solving for x, we find:
x = 3 or x = 4
Now we substitute these values of x into one of the original equations to solve for y.
For x = 3:
y = 3(3) - 4 = 5
For x = 4:
y = 3(4) - 4 = 8
Therefore, the solutions to the system are (3, 5) and (4, 8).