Use the graph to find the solution to this system of linear equations: y = 0.3x + 2.6 and y = 2x + 6.

Steps to Solve

1. 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: $y = -x + 1$

2. Set the equations equal to each other Since both equations equal $y$, we can set them equal to solve for $x$: $$ 2x + 3 = -x + 1 $$

3. 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 $3$:
   $$ x = -\frac{2}{3} $$

4. 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:
   $$ y = -\frac{4}{3} + \frac{9}{3} = \frac{5}{3} $$

5. State the intersection point The intersection point of the two lines is given by the coordinates $(x, y)$. Thus, we have: $$ \left(-\frac{2}{3}, \frac{5}{3}\right) $$