To solve the system of equations using the substitution method, we can substitute the expression for \(y\) from the second equation into the first equation.
We have the equations:
- \(y = x^2 - 4x + 8\)
- \(y = 3x - 4\)
Substituting \(3x - 4\) for \(y\) in the first equation:
\[ 3x - 4 = x^2 - 4x + 8 \]
Now, rearranging the equation:
\[ 0 = x^2 - 4x - 3x + 8 + 4 \ 0 = x^2 - 7x + 12 \]
Next, we can factor the quadratic:
\[ 0 = (x - 3)(x - 4) \]
Setting each factor to zero gives:
\[ x - 3 = 0 \quad \text{or} \quad x - 4 = 0 \]
Thus, \(x = 3\) or \(x = 4\).
Now we can find the corresponding \(y\) values for each \(x\):
-
For \(x = 3\): \[ y = 3(3) - 4 = 9 - 4 = 5 \quad \Rightarrow \quad (3, 5) \]
-
For \(x = 4\): \[ y = 3(4) - 4 = 12 - 4 = 8 \quad \Rightarrow \quad (4, 8) \]
So the solutions to the system are \( (3, 5) \) and \( (4, 8) \).
Therefore, the correct response is:
(4,8) and (3,5) left parenthesis 4 comma 8 right parenthesis and left parenthesis 3 comma 5 right parenthesis