Solve for X and Y Using Substitution: System of Equations with x + y = 5 and 2x - 3y = -15

To solve this system using the substitution method, we'll follow these steps:

• Step 1: Solve the first equation for one variable.

• Step 2: Substitute this expression into the second equation.

• Step 3: Solve for the second variable.

• Step 4: Use the value of the second variable to find the first variable.

Step 1: Solve the first equation $x + y = 5$ for $y$.
We have: $y = 5 - x$.

Step 2: Substitute $y = 5 - x$ into the second equation $2x - 3y = -15$.
This gives us: $2x - 3(5 - x) = -15$.

Step 3: Simplify and solve for $x$:
$\begin{aligned} 2x - 15 + 3x &= -15 \\ 5x - 15 &= -15 \\ 5x &= 0 \\ x &= 0. \end{aligned}$

Step 4: Substitute $x = 0$ back into $y = 5 - x$ to find $y$.
$\begin{aligned} y &= 5 - 0 \\ y &= 5. \end{aligned}$

Thus, the solution to the system of equations is $x = 0$ and $y = 5$.

The correct answer from the list of choices is: $x = 0, y = 5$