How do you solve the system of equations 2x – y = 3 and 4x + 2y = 2 using a graph?

To solve the system of equations 2x – y = 3 and 4x + 2y = 2 using a graph, follow these steps:

1. Rewrite the equations in slope-intercept form:
   For the first equation, isolate y:
   2x – y = 3 ⇒ y = 2x – 3
   For the second equation, also isolate y:
   4x + 2y = 2 ⇒ 2y = -4x + 2 ⇒ y = -2x + 1
2. Plot the first equation:
   Using the equation y = 2x – 3, find two points to graph this line. For instance:
   – If x = 0, then y = -3, giving the point (0, -3).
   – If x = 2, then y = 1, giving the point (2, 1).
   Plot these points and draw a line through them.
3. Plot the second equation:
   Using the equation y = -2x + 1, find two points to graph this line. For instance:
   – If x = 0, then y = 1, giving the point (0, 1).
   – If x = 1, then y = -1, giving the point (1, -1).
   Plot these points and draw a line through them.
4. Identify the intersection point:
   The solution to the system of equations is the point where the two lines intersect. Visually inspect your graph to find this intersection. The coordinates of this point give you the values of x and y that solve the equations.

After plotting, you should see that the lines intersect at a specific point, which represents the solution to the system of equations.