Of course! Let's solve the system of linear equations step-by-step to determine the correct solution from the given options.
We have the system of equations:
1. [tex]\( x + y = 4 \)[/tex]
2. [tex]\( x - y = 6 \)[/tex]
### Step 1: Add the equations
First, we will add the two equations together to eliminate [tex]\( y \)[/tex]:
[tex]\[
(x + y) + (x - y) = 4 + 6
\][/tex]
Simplify the left side:
[tex]\[
x + y + x - y = 10
\][/tex]
[tex]\[
2x = 10
\][/tex]
### Step 2: Solve for [tex]\( x \)[/tex]
Divide both sides by 2:
[tex]\[
x = \frac{10}{2}
\][/tex]
[tex]\[
x = 5
\][/tex]
### Step 3: Substitute [tex]\( x \)[/tex] back into one of the original equations to solve for [tex]\( y \)[/tex]
We can use the first equation [tex]\( x + y = 4 \)[/tex]:
[tex]\[
5 + y = 4
\][/tex]
Subtract 5 from both sides:
[tex]\[
y = 4 - 5
\][/tex]
[tex]\[
y = -1
\][/tex]
### Conclusion:
The solution to the system of equations is [tex]\( x = 5 \)[/tex] and [tex]\( y = -1 \)[/tex]. Thus, the solution is [tex]\( (5, -1) \)[/tex].
### Verify with given options:
The correct option is:
- [tex]\( (5, -1) \)[/tex]
