Let's plot the points and connect them with a line.
We want point (-1,5) to be our solution. This means that we need to find another line that passes through (-1,5). To do this, let's choose the slope of the second line to be -1.
y= -1x+b ⇒ y=- x+b
Now, we will substitute the point ( -1, 5) into the above equation to find the y-intercept b.
The value of b is 4. Now we are ready to complete the second equation and write our example system.
y=-3x+2 & (I) y=- x+ 4 & (II)
Let's add the second line to our graph. We will use a table of values to find points that lie on the line.
x
y=- x+4
y
(x,y)
-1
y=-( -1)+4
5
( -1, 5)
0
y=-( 0)+4
4
( 0, 4)
1
y=-( 1)+4
3
( 1, 3)
Let's plot the points and connect them with a line.
Notice that this is only an example solution, as we can think of many other systems that satisfy the conditions.
