Sure! Let's solve the system of equations using the elimination method.
We have the following system of equations:
1) [tex]\( x - y = 5 \)[/tex]
2) [tex]\( x + y = 3 \)[/tex]
To use the elimination method, we need to add the two equations together in such a way that one of the variables gets eliminated. Let's add the two equations:
[tex]\[
(x - y) + (x + y) = 5 + 3
\][/tex]
Combining like terms, we get:
[tex]\[
x - y + x + y = 8
\][/tex]
This simplifies to:
[tex]\[
2x = 8
\][/tex]
Now, solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{8}{2} = 4
\][/tex]
So we have [tex]\( x = 4 \)[/tex].
Next, we need to find the value of [tex]\( y \)[/tex]. We can substitute [tex]\( x = 4 \)[/tex] back into either of the original equations. Let's use the second equation:
[tex]\[
x + y = 3
\][/tex]
Substitute [tex]\( x = 4 \)[/tex]:
[tex]\[
4 + y = 3
\][/tex]
Now, solve for [tex]\( y \)[/tex] by subtracting 4 from both sides:
[tex]\[
y = 3 - 4 = -1
\][/tex]
So we have [tex]\( y = -1 \)[/tex].
Therefore, the solution to the system of equations is:
[tex]\[
x = 4 \quad \text{and} \quad y = -1
\][/tex]
In other words, the solution in ordered pair form is [tex]\((4, -1)\)[/tex].
