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.