Is $$ (3,2) $$ a solution to the system $$ y-x=1 $$ and $$ -3 x-2 y=5 $$ ? No, because $$ (3,2) $$ is a solution to only one equation. No, because $$ (3,2) $$ is a solution to neither equation. Yes, because $$ (3,2) $$ is a solution to one equation. Yes, because $$ (3,2) $$ is a solution to both equations.

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UpStudy AI · Accepted Answer

To determine whether the point $$ (3, 2) $$ is a solution to the system of equations:

1. $$ y - x = 1 $$
2. $$ -3x - 2y = 5 $$

**Let's evaluate each equation separately:**

1. **First Equation:**
   $$
   y - x = 1 \
   2 - 3 = -1 \neq 1
   $$
   The point $$ (3, 2) $$ does **not** satisfy the first equation.

2. **Second Equation:**
   $$
   -3x - 2y = 5 \
   -3(3) - 2(2) = -9 - 4 = -13 \neq 5
   $$
   The point $$ (3, 2) $$ does **not** satisfy the second equation either.

Since $$ (3, 2) $$ does not satisfy **either** of the equations in the system, it is **not** a solution to the system.

**Correct Answer:**
- **No, because $$ (3,2) $$ is a solution to neither equation.**
$$ (3,2) $$ is not a solution to the system because it does not satisfy either equation.

Is a solution to the system and ?
No, because is a solution to only one equation.
No, because is a solution to neither equation.
Yes, because is a solution to one equation.
Yes, because is a solution to both equations.

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