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
Yes, the solution satisfies at least one of the equations.
Yes, the solution satisfies both equations.
No, the solution satisfies only one of the equations.
No, the solution does NOT satisfy any of the equations.
Line A 2x+5y=9
Line B -x+3=9
Yes, the solution satisfies at least one of the equations.
Yes, the solution satisfies both equations.
No, the solution satisfies only one of the equations.
No, the solution does NOT satisfy any of the equations.
Answers
GPT-4o mini
To determine whether the point (-3, 3) satisfies the equations of the lines in the system, we will substitute \( x = -3 \) and \( y = 3 \) into both equations.
**1. Check Line A: \( 2x + 5y = 9 \)**
Substituting \( x = -3 \) and \( y = 3 \):
\[
2(-3) + 5(3) = -6 + 15 = 9
\]
This equation is satisfied.
**2. Check Line B: \( -x + 3 = 9 \)**
Substituting \( x = -3 \):
\[
-(-3) + 3 = 3 + 3 = 6
\]
This equation is **not** satisfied.
Since the solution (-3, 3) satisfies Line A but does not satisfy Line B, the correct conclusion is:
**No, the solution satisfies only one of the equations.**
**1. Check Line A: \( 2x + 5y = 9 \)**
Substituting \( x = -3 \) and \( y = 3 \):
\[
2(-3) + 5(3) = -6 + 15 = 9
\]
This equation is satisfied.
**2. Check Line B: \( -x + 3 = 9 \)**
Substituting \( x = -3 \):
\[
-(-3) + 3 = 3 + 3 = 6
\]
This equation is **not** satisfied.
Since the solution (-3, 3) satisfies Line A but does not satisfy Line B, the correct conclusion is:
**No, the solution satisfies only one of the equations.**