Question
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:
-
Substitute
in the second equation: -
Solve for
: -
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!