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Solve System of Equations: 2x + y = 8, x - y = 1
Published on October 7, 2024
Algebra
Solve the system of equations 2x + y = 8 and x - y = 1. The solution is x = 3 and y = 2.
Question
Solve the system of equations: 2x + y = 8 x - y = 1
Answer
Here’s how to solve the system of equations step-by-step:
1. Elimination Method
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Notice that the ‘y’ coefficients have opposite signs. This makes it easy to eliminate ‘y’ by adding the equations together.
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Add the equations:
(2x + y) + (x - y) = 8 + 1 -
Simplify:
3x = 9 -
Solve for ‘x’:
x = 3
2. Substitution
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Now that we know x = 3, substitute it into either of the original equations to solve for ‘y’. Let’s use the first equation:
2(3) + y = 8 -
Simplify:
6 + y = 8 -
Solve for ‘y’:
y = 2
Answer:
The solution to the system of equations is x = 3 and y = 2. This can also be written as the ordered pair (3, 2).
The solution to the system of equations is x = 3 and y = 2. This can also be written as the ordered pair (3, 2).