Solve the following system of equations graphically on the set of axes below.
y = 2x – 1
x + 2y = 8
Plot two lines by clicking the graph.
Click a line to delete it.
Solve the following system of equations graphically on the set of axes below. y = 2x – 1 x + 2y = 8 Plot two lines by clicking the graph. Click a line to delete it.
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To solve the system of equations graphically, we need to plot the two lines represented by the equations:
1. Equation 1: ( y = 2x – 1 )
This is in slope-intercept form (y = mx + b), where the slope (m) is 2 and the y-intercept (b) is -1.
To plot this line:
– Start at the y-intercept, point (0, -1).
– Use the slope to find another point. From (0, -1), move up 2 units and right 1 unit to get to (1, 1).
– Draw the line through these points.
2. Equation 2: ( x + 2y = 8 )
Rearranging this into slope-intercept form gives us ( 2y = -x + 8 ) or ( y = -frac{1}{2}x + 4 ).
Here, the slope is -1/2, and the y-intercept is 4.
To plot this line:
– Start at the y-intercept, point (0, 4).
– Use the slope to find another point. From (0, 4), move down 1 unit and right 2 units to get to (2, 3).
– Draw the line through these points.
Next, look for the point where the