Use the graph to find the solution to this system of linear equations: y = 0.3x + 2.6 and y = 2x + 6.
Understand the Problem
The question requires us to find the point where the two linear equations intersect on a coordinate plane. This involves identifying the coordinates that satisfy both equations simultaneously.
Answer
The intersection point is \(\left(\frac{2}{3}, \frac{5}{3}\right)\).
Answer for screen readers
The intersection point of the two equations is (\left(\frac{2}{3}, \frac{5}{3}\right)).
Steps to Solve

Identify the equations We need to identify the two linear equations that we will work with. Let's say the equations are: Equation 1: $y = 2x + 3$
Equation 2: $y = x + 1$ 
Set the equations equal to each other Since both equations equal $y$, we can set them equal to solve for $x$: $$ 2x + 3 = x + 1 $$

Solve for $x$ Now, we will rearrange to isolate $x$. First, add $x$ to both sides: $$ 2x + x + 3 = 1 $$
This simplifies to:
$$ 3x + 3 = 1 $$
Next, subtract $3$ from both sides:
$$ 3x = 1  3 $$
Thus,
$$ 3x = 2 $$
Finally, divide by $3$:
$$ x = \frac{2}{3} $$ 
Substitute $x$ back into one of the original equations Now we will substitute $x = \frac{2}{3}$ back into one of the original equations to find $y$. We'll use Equation 1: $$ y = 2\left(\frac{2}{3}\right) + 3 $$
This simplifies to:
$$ y = \frac{4}{3} + 3 $$
To combine the fractions, note that $3 = \frac{9}{3}$, so:
$$ y = \frac{4}{3} + \frac{9}{3} = \frac{5}{3} $$ 
State the intersection point The intersection point of the two lines is given by the coordinates $(x, y)$. Thus, we have: $$ \left(\frac{2}{3}, \frac{5}{3}\right) $$
The intersection point of the two equations is (\left(\frac{2}{3}, \frac{5}{3}\right)).
More Information
Finding the intersection of two lines gives us the point where they meet, which can represent a solution to a system of equations in various applications like economics, physics, or realworld situations.
Tips
 Not correctly setting the equations equal to each other; ensure both equations are in the same format.
 Errors in basic arithmetic while combining or simplifying equations; doublecheck each calculation.