Question

This system has one solution. Type the y-coordinate of the solution in the box.


y
=
x
2
-
3
x
+
7
y
=
3
x
-
2

Answer 1

To find the y-coordinate of the solution of the given system of equations, we have:

1) \( y = x^2 - 3x + 7 \)

2) \( y = 3x - 2 \)

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

\[
x^2 - 3x + 7 = 3x - 2
\]

Now, we will rearrange the equation:

\[
x^2 - 3x - 3x + 7 + 2 = 0
\]

Simplifying that gives:

\[
x^2 - 6x + 9 = 0
\]

This can be factored as:

\[
(x - 3)^2 = 0
\]

So, the solution for \( x \) is:

\[
x = 3
\]

Now we can substitute \( x = 3 \) back into either of the original equations to find the y-coordinate. Let's use the second equation:

\[
y = 3(3) - 2
\]
\[
y = 9 - 2
\]
\[
y = 7
\]

Thus, the y-coordinate of the solution is:

\[
\boxed{7}
\]