y = x - 4; y = 6x - 10
Understand the Problem
The question seems to present two linear equations, and it is likely asking to find the point of intersection or to solve them in some manner.
Answer
The point of intersection is $\left(\frac{6}{5}, \frac{-14}{5}\right)$.
Answer for screen readers
The point of intersection is $\left(\frac{6}{5}, \frac{-14}{5}\right)$.
Steps to Solve
- Set the equations equal to each other
Since both equations equal $y$, we can set them equal to each other: $$ x - 4 = 6x - 10 $$
- Rearrange the equation
Next, let's isolate $x$ by getting all $x$ terms on one side and constant terms on the other side: $$ x - 6x = -10 + 4 $$ This simplifies to: $$ -5x = -6 $$
- Solve for $x$
Now, divide both sides by -5 to find $x$: $$ x = \frac{-6}{-5} = \frac{6}{5} $$
- Substitute $x$ back into one of the original equations
Now we will substitute $x = \frac{6}{5}$ back into the first equation to find $y$: $$ y = x - 4 = \frac{6}{5} - 4 = \frac{6}{5} - \frac{20}{5} = \frac{-14}{5} $$
- Conclude with the point of intersection
Thus, the point of intersection of the two equations is: $$ \left(\frac{6}{5}, \frac{-14}{5}\right) $$
The point of intersection is $\left(\frac{6}{5}, \frac{-14}{5}\right)$.
More Information
The equations represent two lines in a coordinate plane, and their intersection point indicates where both lines meet. This is useful in various applications like solving system of equations in algebra.
Tips
- Overlooking the need to simplify when combining like terms.
- Miscalculating signs when moving terms from one side to another.
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