Question

What did I do wrong

Answer 1

To solve a system of equations by graphing, you must first graph both equations. The solution is the point of intersection of the lines.

To plot these two equations, do this.

First equation.
y = 3x + 1
y = mx + b
b = 1, so plot point (0, 1), the y-intercept.
Now starting at point (0, 1), use the slope, m = 3 = 3/1, to go up 3 units and 1 unit to the right. Plot that point which is (1, 4). Now connect points (0, 1) and (1, 4) with a straight line and extend the line in both directions. That is how you graph the first equation.

Second equation.
Solve it for y.

x - 2y = 8

-2y = -x + 8

y = (1/2)x - 4

y = mx + b

b = -4. Plot point (0, -4) which is the y-intercept. Now from that point, go up 1 unit and right 2 units to point (2, -3), and plot that point. Connect the two points with a straight line and extend it in both directions. That is how you plot the second equation.

The point of intersection of both lines is the solution of the system of equations. Read that point.