Let's plot the points and connect them with a line.
Let's choose point (0,1) to be our solution since it lies on the line. This means that we need to find another line that passes through (0,1). To do this, let's choose the slope of the second line to be 2.
y= 2x+b
Now, we will substitute the point ( 0, 1) into the above equation to find y-intercept b.
The value of b is 1. Now we are ready to complete the second equation and write our example system.
y=-9x+1 & (I) y=2x+ 1 & (II)
Let's add the second line to our graph. We will again use a table of values to find points that lie on the line.
x
y=2x+1
y
(x,y)
-1
y=2( -1)+1
-1
( -1, -1)
0
y=2( 0)+1
1
( 0, 1)
1
y=2( 1)+1
3
( 1, 3)
Let's plot the points and connect them with a line.
Notice that this is only example solution, as we can think of many other systems that will have a solution that lies on line y=2x+1. Also, such a system does not need to contain this equation to have a solution that lies on its line.
