Pregunta
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Responder
The solution to the system of equations is
and
.
Solución
To solve the system of equations:
Let’s use the addition method to eliminate one of the variables.
Step 1: Add the Two Equations
Add equation (1) and equation (2) together to eliminate
:
Step 2: Solve for
Step 3: Substitute
Back into One of the Original Equations
Let’s substitute
into equation (1):
Solution
The solution to the system of equations is:
Verification
It’s always good practice to verify the solution by plugging the values back into both original equations.
- First Equation:
- Second Equation:
Both equations are satisfied, confirming that
and
is the correct solution.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Mind Expander
Let’s dive into the history of linear equations! These algebraic equations have been around since ancient civilizations. The earliest recorded use is attributed to the Babylonians around 2000 BCE, who solved linear equations to manage trade and land distribution. Fast forward to the 19th century, and you find mathematicians like Augustin-Louis Cauchy and Évariste Galois laying down the groundwork for modern algebraic structures.
Now, let’s tackle some problem-solving tips! When solving systems of equations like the one you provided, it’s often helpful to use either the substitution method or the elimination method. In this case, you could eliminate
by adding the two equations together, or isolate
from one equation and substitute it into the other. Don’t forget to double-check your solutions; a common mistake is minor calculation errors that can lead to incorrect results!
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