x-y=1 x+y=7 solve for the following system of equations by graphing
To solve the system of equations by graphing, we will plot the graphs of the two equations on a coordinate plane and find the point of intersection, which represents the solution to the system.
First, let's rearrange the given equations:
x - y = 1 --> y = x - 1
x + y = 7
Now, let's create a table of values for each equation:
For the equation y = x - 1:
x | y
--------
0 | -1
1 | 0
2 | 1
For the equation x + y = 7:
x | y
--------
0 | 7
1 | 6
2 | 5
Now, let's plot the points for both equations on a coordinate plane:
x-y=1 (blue line)
(x,y) points: (0,-1), (1,0), (2,1)
x+y=7 (red line)
(x,y) points: (0,7), (1,6), (2,5)
Now, let's draw the lines passing through these points:
{{{graph(400,400,-5,5,-5,10,x-1,7-x)}}}
From the graph, we can see that the two lines intersect at the point (4,3). Therefore, the solution to the system of equations is x = 4 and y = 3.