How to solve one - variable linear equation.
I. `2x+3y=8`
II. `3x+2y=7`

Answer

To solve the system of equations given by:

I. \( 2x + 3y = 8 \)
II. \( 3x + 2y = 7 \)

we will use the method of elimination to find the values of \( x \) and \( y \).

### Step 1: Align the equations
We have the two equations:
1. \( 2x + 3y = 8 \) (Equation 1)
2. \( 3x + 2y = 7 \) (Equation 2)

### Step 2: Eliminate one variable
To eliminate one of the variables, we can multiply the equations by suitable numbers so that the coefficients of one variable are the same.

Let's eliminate \( x \). The coefficient of \( x \) in Equation 1 is 2 and in Equation 2 is 3. We can multiply Equation 1 by 3 and Equation 2 by 2:

- Multiply Equation 1 by 3:
\[ 3(2x + 3y) = 3(8) \implies 6x + 9y = 24 \quad \text{(Equation 3)} \]

- Multiply Equation 2 by 2:
\[ 2(3x + 2y) = 2(7) \implies 6x + 4y = 14 \quad \text{(Equation 4)} \]

### Step 3: Subtract the equations
Now we have:
1. \( 6x + 9y = 24 \) (Equation 3)
2. \( 6x + 4y = 14 \) (Equation 4)

Subtract Equation 4 from Equation 3:
\[ (6x + 9y) - (6x + 4y) = 24 - 14 \]
This simplifies to:
\[ 5y = 10 \]

### Step 4: Solve for \( y \)
Now, divide both sides by 5:
\[ y = \frac{10}{5} = 2 \]

### Step 5: Substitute \( y \) back to find \( x \)
Now that we have \( y = 2 \), we can substitute this value back into either of the original equations to find \( x \). Let's use Equation 1:
\[ 2x + 3(2) = 8 \]
This simplifies to:
\[ 2x + 6 = 8 \]
Subtract 6 from both sides:
\[ 2x = 2 \]
Now divide by 2:
\[ x = 1 \]

### Final Solution
The solution to the system of equations is:
\[ x = 1, \quad y = 2 \]