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solve the linear system by graphing and check the solution

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2 Answers

Hi L;
The format of these equations is...
y=mx+b
m is the slope.  Slope is also called rise-over-run--the change of y divided by the change of x.
b is the y-intercept, the value of y when x=0.
 
y= x + 1
slope--m=1
y-intercept--b=1
This line has a positive slope of 1.  As the value of y increases by one unit, the value of x increases by one unit.
At the point of (0,1), this line crosses the y-axis.

y= -3x + 9
This line has a negative slope of 3.  Normally, this would be written as -3/1.  In this circumstance, the field of mathematics contradicts itself.  It is actually 3/-1.  As the value of y increases three units, the value of x decreases by one unit.
At the point of (0,9), this line crosses the y-axis.
 
We have established one point as well as the slope of each line.  This should be adequate to graph each line.  It would be nice if we also know at what point these lines intersect...
y= x + 1
y= -3x + 9
 
Let's subtract the latter equation from the first...
y= x + 1
-(y= -3x + 9)
0=4x-8
-4x=-8
x=2
 
Let's establish the value of y...
y= x + 1
y=2+1
y=3
The lines intersect at (2,3).
Let's verify this with the other equation...
y= -3x + 9
3=-3(2)+9
3=-6+9
3=3
 Y = X +1
 Y =  - 3X +9                        Graph both lines by connecting the intercept points:
 
                                              Y = X +1      ( 0, 1)   ( 1, 0)
 
                                              
                                              Y = -3X + 9      ( 0 , 9 ) ( 3 , 0 )
 
          X - Y = -1                      intersection point of 2 lines should be ( 2 , 3 )
         3 X + y = 9   
   
         4 X = 8     X = 2 
 
         Y = 2 +1 = 3