How to Solve a System of Equations with Fractions

TL;DR

To solve the system of equations 10/x + 9/y = 2 and 7/x - 6/y = 11/2, use the elimination method by multiplying the first equation by 2 and the second by 3. This yields X = 2 and Y = -3, resulting in the solution as the ordered pair (2, -3).

Transcript

hello in this video we're going to solve a system of equations we have 10 over X Plus 9 over y equals 2 and 7 over x minus 6 over y equals 11 over 2. let's go ahead and work through it solution I'm thinking we can use something called the elimination method and we can use it to eliminate these terms here so if we multiply the first equation by 2 . ... Read More

Key Insights

• ❓ The elimination method is a useful technique in solving systems of equations efficiently.
• 🍉 Multiplying and adding equations strategically can cancel out terms and simplify the solving process.
• 😑 Expressing the final solution as an ordered pair ensures clarity and accuracy in presenting the solution.

Questions & Answers

Q: What method was used to solve the system of equations in the video?

The elimination method was used in the video to solve the system of equations. By multiplying and adding equations strategically, terms were eliminated to find the values of X and Y.

Q: How were the equations manipulated to eliminate terms during the solving process?

The first equation was multiplied by 2, and the second equation by 3 to ensure the terms to be canceled out upon addition. This manipulation allowed for a straightforward calculation.

Q: What are the final values of X and Y obtained after solving the system of equations?

After solving the equations, X was determined to be 2 and Y to be -3. These values were derived by substituting X into one of the original equations and solving for Y.

Q: Why is it suggested to express the solution as an ordered pair (X, Y) in the end?

Expressing the solution as an ordered pair (2, -3) provides a clear and concise representation of the values of X and Y that satisfy both equations, confirming the accuracy of the solution.

Summary & Key Takeaways

• Utilizing the elimination method to solve a system of equations with X = 2 and Y = -3.

• Multiplying and adding equations to cancel out terms and solve for X and Y values.

• Final solution: X = 2, Y = -3, presented as an ordered pair (2, -3).