Sure, let's solve the system of equations using the elimination method step-by-step:
Given system of equations:
1) [tex]\( x - y = 5 \)[/tex]
2) [tex]\( x + y = 3 \)[/tex]
Step 1: Add the two equations to eliminate [tex]\( y \)[/tex].
When we add equations (1) and (2), we get:
[tex]\[
(x - y) + (x + y) = 5 + 3
\][/tex]
This simplifies to:
[tex]\[
x - y + x + y = 8
\][/tex]
Combining like terms, we have:
[tex]\[
2x = 8
\][/tex]
Step 2: Solve for [tex]\( x \)[/tex].
Divide both sides by 2:
[tex]\[
x = \frac{8}{2}
\][/tex]
So:
[tex]\[
x = 4
\][/tex]
Step 3: Substitute [tex]\( x = 4 \)[/tex] back into one of the original equations to solve for [tex]\( y \)[/tex].
Let's use equation (1):
[tex]\[
x - y = 5
\][/tex]
Substituting [tex]\( x = 4 \)[/tex]:
[tex]\[
4 - y = 5
\][/tex]
Step 4: Solve for [tex]\( y \)[/tex].
Subtract 4 from both sides:
[tex]\[
-y = 1
\][/tex]
Multiplying both sides by -1:
[tex]\[
y = -1
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
x = 4 \quad \text{and} \quad y = -1
\][/tex]
The ordered pair [tex]\((4, -1)\)[/tex] represents the solution.
