Hello, The solution to the given pair of linear equations is x = 5 and y = 3.

Step-by-Step Solution

We can solve this system of equations using the elimination method .

1. Write Down the Equations

First, let's rearrange the equations into a standard format:

1. x + y = 8

2. 2x - 3y = 1

2. Prepare for Elimination

To eliminate the variable 'y', we need its coefficient to be the same (but with an opposite sign) in both equations. We can achieve this by multiplying the first equation by 3.

3

times( x+y = 8 )

implies3x + 3y = 24

Now we have our new system of equations:

• 3x + 3y = 24
• 2x - 3y = 1

3. Add the Equations

Now, add the two modified equations together. The 'y' terms will cancel each other out.

3x + 3y = 24

+ 2x - 3y = 1

----------------

5x + 0  = 25

This simplifies to:

5x = 25

4. Solve for x

Divide both sides by 5 to find the value of x:

x = 25 / 5

x = 5

5. Solve for y

Substitute the value of x (which is 5) back into the simplest original equation (x + y = 8) to find y.

5 + y = 8y = 8 - 5y = 3

The final answer is x = 5 and y = 3.