Question
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Consider the following two linear equations.
Solve for the point of intersection using substitution (8)

Ask by Adkins Collins. in Guinea
Jan 19,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Cannot determine the point of intersection without a second equation.

Solution

To find the point of intersection of the two linear equations, we will use substitution. However, it seems that only one equation is provided. For a complete solution, we need a second equation.
Assuming the second equation is (where and are constants), we can proceed with the substitution method.
Let’s denote the first equation as:
Now, if we had a second equation, we would substitute the expression for from the first equation into the second equation.
For example, if the second equation were , we would substitute as follows:
  1. Substitute in the second equation:
  2. Solve for :
  3. Substitute back into the first equation to find :
Thus, the point of intersection would be .
Please provide the second equation so I can solve for the exact point of intersection.

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Extra Insights

To find the point of intersection of the equations, you can use substitution. First, we need another equation. If we take the equation , let’s create a second linear equation. For example, let’s consider .
Now, substitute for in the second equation:
Combine like terms:
Now substitute back into the first equation to find :
So, the point of intersection is .
Know that many linear equations can represent real-world scenarios! For instance, in economics, linear equations can model supply and demand. Finding the point of intersection helps determine the equilibrium price and quantity in a market, showcasing how math seamlessly integrates into daily life!
If you’re solving linear equations, make sure to carefully check your arithmetic! A common mistake is misplacing a negative sign. Always double-check your calculations step by step to avoid those sneaky errors that can lead to incorrect intersection points! Happy solving!

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