Question

Evelyn graphed the following system and determined the solution to the systen is (-3,3)
Line A 2x+5y=9
Line B -x+3=9

Answer 1

To verify whether the point (-3, 3) is indeed the solution to the given system of equations, we need to substitute \(x = -3\) and \(y = 3\) into both equations and check if they hold true.

### Line A: \(2x + 5y = 9\)
Substituting \((-3, 3)\):
\[
2(-3) + 5(3) = 9
\]
Calculating the left side:
\[
-6 + 15 = 9
\]
\[
9 = 9 \quad \text{(True)}
\]

### Line B: \(-x + 3 = 9\)
Substituting \(x = -3\):
\[
-(-3) + 3 = 9
\]
Calculating the left side:
\[
3 + 3 = 9
\]
\[
6 \neq 9 \quad \text{(False)}
\]

### Conclusion
The point (-3, 3) satisfies Line A but does not satisfy Line B. Therefore, (-3, 3) is not a solution for the given system of equations.

Let's determine if there is a different solution by solving the system of equations correctly.

### Solve for Line B
First, let's rewrite Line B \(-x + 3 = 9\):
\[
-x = 9 - 3
\]
\[
-x = 6
\]
\[
x = -6
\]

Now, substitute \(x = -6\) into Line A to find \(y\):
### Line A: \(2x + 5y = 9\)
\[
2(-6) + 5y = 9
\]
\[
-12 + 5y = 9
\]
\[
5y = 9 + 12
\]
\[
5y = 21
\]
\[
y = \frac{21}{5} = 4.2
\]

### Solution
The actual solution to the system of equations is \((-6, 4.2)\). The solution provided by Evelyn, (-3, 3), is incorrect.