Pregunta
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Ask by May Sanders. in the United States
Jan 23,2025

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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.
  1. First Equation:
  2. Second Equation:
Both equations are satisfied, confirming that and is the correct solution.

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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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