Which of the following uses the substitution method to solve linear-quadratic system y=x2−4x+8 , y=3x−4 ?(1 point)Responses(4,8)left parenthesis 4 comma 8 right parenthesis(4,8) and (3,5)left parenthesis 4 comma 8 right parenthesis and left parenthesis 3 comma 5 right parenthesis(3,5)left parenthesis 3 comma 5 right parenthesis(−4,−16) and (−3,−13)
To use the substitution method, we will substitute the value of y from the second equation into the first equation.
We have the second equation: y = 3x - 4
Substituting this into the first equation, we get: 3x - 4 = x^2 - 4x + 8
Rearranging this equation, we get: x^2 - 7x + 12 = 0
Now we can factor this equation: (x - 3)(x - 4) = 0
Setting each factor equal to zero, we get: x - 3 = 0 and x - 4 = 0
This gives us two possible values for x: x = 3 and x = 4
Substituting these values back into the second equation, we can find the corresponding y values:
For x = 3, we have: y = 3(3) - 4 = 9 - 4 = 5
For x = 4, we have: y = 3(4) - 4 = 12 - 4 = 8
Therefore, the solution to the linear-quadratic system using the substitution method is the points (3, 5) and (4, 8). Option (3,5) and option (4,8) both represent this solution.