Question

Giovanni graphed the following sysytem of equations . he says that (2.5, 4.5) is the solution. what is one way you can use substitution to see if giovanni is correct

Answer 1

To check if the point (2.5, 4.5) is a solution to the system of equations using substitution, you need to follow these steps:

1. **Identify the system of equations**: Make sure you have the two equations that Giovanni graphed.

2. **Substitute the point into the equations**: Take the x-coordinate (2.5) and the y-coordinate (4.5) from the point (2.5, 4.5) and substitute them into both equations.

3. **Check each equation**:
- For the first equation, substitute \( x = 2.5 \) and \( y = 4.5 \).
- Simplify the equation to see if it holds true (equals a true statement).
- Repeat this for the second equation.

4. **Conclusion**: If (2.5, 4.5) satisfies both equations (i.e., both equations are true after substitution), then Giovanni is correct. If either equation does not hold true, then (2.5, 4.5) is not a solution to the system.

### Example
Suppose the system of equations is:
1. \( y = 2x + 1 \)
2. \( y = -x + 7 \)

**Substituting into the first equation**:

\[
4.5 = 2(2.5) + 1 \\
4.5 = 5 + 1 \\
4.5 = 6 \quad (\text{False})
\]

**Substituting into the second equation**:

\[
4.5 = -2.5 + 7 \\
4.5 = 4.5 \quad (\text{True})
\]

Since the first equation is false, Giovanni's solution (2.5, 4.5) is not correct.

You can perform similar checks with your specific equations to see if Giovanni's point is a solution.