To solve a system of linear equations, we can use either the substitution method or the elimination method. Below is an example of a common system and its solution:
Example System of Equations
Suppose the system is:
- (x + y = 5)
- (2x - y = 1)
Step 1: Use Elimination Method
Add the two equations to eliminate (y):
[
(x + y) + (2x - y) = 5 + 1 \
3x = 6 \
x = 2
]
Step 2: Substitute (x = 2) into Equation 1
[
2 + y = 5 \
y = 5 - 2 = 3
]
Solution: (\boxed{(2, 3)})
If your system differs, apply the same logic: either substitute one variable into the other equation or eliminate a variable by adding/subtracting scaled equations. The key is to find values of (x) and (y) that satisfy both equations simultaneously.
For most standard systems similar to the example above, the solution is (\boxed{(2,3)}).
Answer: (\boxed{(2, 3)})
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