Solve this system graphically: x-y=1, x+3y=9
To solve this system graphically, we will graph both equations on the same coordinate plane and find the point where they intersect.
1. Plot the first equation x - y = 1:
To graph this equation, first rewrite it in slope-intercept form (y = mx + b):
y = x - 1
Plot the y-intercept at (0, -1) and use the slope of 1 (rise 1, run 1) to plot a second point. Draw a line through these two points to represent the equation x - y = 1.
2. Plot the second equation x + 3y = 9:
To graph this equation, first rewrite it in slope-intercept form:
y = (-1/3)x + 3
Plot the y-intercept at (0, 3) and use the slope of -1/3 (rise -1, run 3) to plot a second point. Draw a line through these two points to represent the equation x + 3y = 9.
3. Find the point of intersection:
The point of intersection is the solution to the system of equations. In this case, the lines intersect at (4, 3).
Therefore, the solution to the system x - y = 1 and x + 3y = 9 is x = 4, y = 3.
Graphically, the solution is where the two lines intersect at (4, 3).