Certainly! Let's solve the system of linear equations step-by-step.
Given the system of equations:
1. \(\( x - y = 2 \)\)
2. \(\( 6x + y = 5 \)\)
### Step 1: Solve Equation 1 for \(\( y \)\)
From the first equation, we can express \(\( y \)\) in terms of \(\( x \)\):
\(\[ x - y = 2 \]\)
Rearrange this to solve for \(\( y \)\):
\(\[ y = x - 2 \]\)
### Step 2: Substitute \(\( y \)\) into Equation 2
Now, we substitute the expression for \(\( y \)\) from Step 1 into the second equation:
\(\[ 6x + y = 5 \]\)
\(\[ 6x + (x - 2) = 5 \]\)
### Step 3: Simplify and Solve for \(\( x \)\)
Combine like terms:
\(\[ 6x + x - 2 = 5 \]\)
This simplifies to:
\(\[ 7x - 2 = 5 \]\)
Add 2 to both sides of the equation to isolate the term with \(\( x \)\):
\(\[ 7x = 7 \]\)
Divide both sides by 7:
\(\[ x = 1 \]\)
### Step 4: Substitute \(\( x \)\) back into the Expression for \(\( y \)\)
Use the value of \(\( x \)\) found in Step 3 to find \(\( y \)\):
\(\[ y = x - 2 \]\)
\(\[ y = 1 - 2 \]\)
\(\[ y = -1 \]\)
### Summary
The solution to the system of equations is:
\(\[ x = 1 \]\)
\(\[ y = -1 \]\)
So, \(\( (x, y) \)\) is \(\( (1.0, -1.0) \)\).
