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