For the two linear functions, find the point of intersection:

x=y+2                2x−3y=−1

To find the point of intersection of the two linear functions, we need to solve the system of equations formed by them:

\[
x = y + 2
\]
\[
2x - 3y = -1
\]

### Step 1: Substitute the expression for \( x \) from the first equation into the second equation.

Since \( x = y + 2 \), substitute this into the second equation:

\[
2(y + 2) - 3y = -1
\]

### Step 2: Simplify and solve for \( y \).

Distribute the 2:

\[
2y + 4 - 3y = -1
\]

Combine like terms:

\[
-y + 4 = -1
\]

Subtract 4 from both sides:

\[
-y = -5
\]

Multiply both sides by -1:

\[
y = 5
\]

### Step 3: Substitute \( y = 5 \) back into the first equation to find \( x \).

Using the first equation \( x = y + 2 \):

\[
x = 5 + 2 = 7
\]

### Step 4: Write the solution.

The point of intersection is \( (x, y) = (7, 5) \).

### Final Answer
The two lines intersect at the point \( (7, 5) \).

Would you like more details or have any questions?

Here are some related questions:
1. What is the graphical interpretation of the point of intersection?
2. How would you verify the solution by substituting the values back into the original equations?
3. How can you solve the system of equations using the elimination method?
4. What happens if the two lines are parallel?
5. Can we find the intersection of two linear functions if one or both are vertical lines?

**Tip:** When solving systems of linear equations, substituting one equation into another is a common method called the substitution method. This technique is particularly useful when one equation is already solved for one variable.

Learn how to find the point of intersection for two linear functions x=y+2 and 2x−3y=−1 with a step-by-step solution. This problem involves solving a system of linear equations using the substitution method. Suitable for high school students (Grades 9-12).

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