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Solving a system of two linear equations
Published on October 26, 2024
Algebra
The solution to the system of equations x + 2y = 5 and 3x - y = 1 is x = 1 and y = 2, found using the elimination method.
Question
x + 2y = 5 3x - y = 1
Answer
We can solve this system of equations using elimination.
Step 1: Manipulate the equations to make the coefficients of one variable opposites.
Multiply the second equation by 2 to make the y coefficients opposites:
This simplifies to:
Step 2: Add the equations together to eliminate one variable.
Adding the two equations, we get:
This simplifies to:
Step 3: Solve for the remaining variable.
Divide both sides by 7:
Step 4: Substitute the value found in Step 3 back into either original equation to solve for the other variable.
Let’s use the first original equation:
Subtract 1 from both sides:
Divide both sides by 2:
Answer: The solution to the system of equations is