To solve the system of equations graphically, follow these steps:
1. Rewrite the equations for convenience:
- Equation 1: [tex]\( y = \frac{1}{4}x + 3 \)[/tex]
- Equation 2: [tex]\( y = 2x + 10 \)[/tex]
2. Identify the slope and y-intercept for each equation:
- Equation 1: Slope [tex]\( m = \frac{1}{4} \)[/tex], y-intercept [tex]\( b = 3 \)[/tex]
- Equation 2: Slope [tex]\( m = 2 \)[/tex], y-intercept [tex]\( b = 10 \)[/tex]
3. Plot the first equation [tex]\( y = \frac{1}{4}x + 3 \)[/tex]:
- Start at the y-intercept (0, 3).
- Using the slope [tex]\( \frac{1}{4} \)[/tex], go up 1 unit and right 4 units from the y-intercept to another point.
- Draw the line connecting these points.
4. Plot the second equation [tex]\( y = 2x + 10 \)[/tex]:
- Start at the y-intercept (0, 10).
- Using the slope [tex]\( 2 \)[/tex], go up 2 units and right 1 unit from the y-intercept to another point.
- Draw the line connecting these points.
5. Identify the intersection point of the two lines:
- Observe where the two lines cross on the graph.
After plotting both lines and identifying their intersection, we determine the solution for the system of equations based on the coordinates of the intersection point. From our steps, the coordinates of the intersection point are:
[tex]\[
x = -4, \quad y = 2
\][/tex]
So, the solution for the system of equations is:
[tex]\[
\boxed{-4}, \boxed{2}
\][/tex]
