Question

Which of the following uses the substitution method to solve linear-quadratic system y=x2−4x+8, y=3x−4?(1 point)
Responses

(−4,−16) and (−3,−13)
left parenthesis negative 4 comma negative 16 right parenthesis and left parenthesis negative 3 comma negative 13 right parenthesis

(3,5)
left parenthesis 3 comma 5 right parenthesis

(4,8)
left parenthesis 4 comma 8 right parenthesis

(4,8) and (3,5)

Answer 1

To solve the system of equations using the substitution method, we have the following equations:

1. \( y = x^2 - 4x + 8 \)
2. \( y = 3x - 4 \)

We can set the two equations equal to each other since both are equal to \( y \):

\[
x^2 - 4x + 8 = 3x - 4
\]

Now we can rearrange this equation to find the values of \( x \):

\[
x^2 - 4x - 3x + 8 + 4 = 0
\]

This simplifies to:

\[
x^2 - 7x + 12 = 0
\]

Next, we can factor this quadratic equation:

\[
(x - 3)(x - 4) = 0
\]

This gives us two possible values for \( x \):

\[
x = 3 \quad \text{or} \quad x = 4
\]

Now, we can find the corresponding \( y \) values for each \( x \) using the second equation \( y = 3x - 4 \):

1. For \( x = 3 \):
\[
y = 3(3) - 4 = 9 - 4 = 5 \quad \Rightarrow \quad (3, 5)
\]

2. For \( x = 4 \):
\[
y = 3(4) - 4 = 12 - 4 = 8 \quad \Rightarrow \quad (4, 8)
\]

Thus, the solutions to the system of equations are \( (3, 5) \) and \( (4, 8) \).

From the options given, the correct answer is:

**(4, 8) and (3, 5)**