Find the intersection point of the lines given by the equations \( y = 2x + 1 \) and \( y = -0.5x + 3 \).

To find the intersection point of the lines given by the equations \( y = 2x + 1 \) and \( y = -0.5x + 3 \), we need to set the two equations equal to each other: \[ 2x + 1 = -0.5x + 3 \] Now, let's solve for \( x \). First, we can add \( 0.5x \) to both sides: \[ 2x + 0.5x + 1 = 3 \] This simplifies to: \[ 2.5x + 1 = 3 \] Next, subtract 1 from both sides: \[ 2.5x = 3 - 1 \] \[ 2.5x = 2 \] Now, divide both sides by 2.5: \[ x = \frac{2}{2.5} = \frac{2 \times 10}{25} = \frac{20}{25} = \frac{4}{5} \] Now that we have \( x = \frac{4}{5} \), we can substitute this value back into either of the original equations to solve for \( y \). Let's use the first equation: \[ y = 2x + 1 \] Substituting \( x = \frac{4}{5} \): \[ y = 2\left(\frac{4}{5}\right) + 1 = \frac{8}{5} + \frac{5}{5} = \frac{13}{5} \] Thus, the intersection point of the lines is: \[ \left( \frac{4}{5}, \frac{13}{5} \right) \]