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Solve the system of equations
.
Solve the system of equations by following steps:
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
- step1: Solve the equation:
- step2: Substitute the value of
- step3: Simplify:
- step4: Move the constant to the right side:
- step5: Subtract the numbers:
- step6: Change the signs:
- step7: Divide both sides:
- step8: Divide the numbers:
- step9: Substitute the value of
- step10: Calculate:
- step11: Calculate:
- step12: Check the solution:
- step13: Rewrite:
The solution to the system of equationsand is and .
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Extra Insights
To understand the beauty of systems of equations, let’s dive into their historical background! The roots of linear equations go back to ancient civilizations, where mathematicians like Babylonian scribes used geometrical methods to solve problems similar to our modern systems. Fast forward to the 17th century, and we have René Descartes who laid down the groundwork for algebra and geometry, bringing us closer to what we use today!
Now, let’s look at real-world applications! Systems of equations are everywhere, from planning production schedules in factories (where you need to balance inputs and outputs) to economics, where they help determine supply and demand. Engineers use these equations to design bridges or buildings, ensuring safety and stability by finding the optimal material distribution. So, next time you solve a system, remember you’re tapping into a rich tapestry of human innovation!