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solve the linear system by graphing

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2 Answers

Graphing linear systems is pretty mindless once you have the process.
1) Find the y intercept where x=0.
y = x + 1 --> (0,1)
y = -3x + 9 --> (0,9)
2) Find the x intercept where y =0
y = x +1 --> (-1,0)
y = -3x + 9 --> (3,0)
3) Draw the appropriate scaling for x and y. We know that y has to go up to 9 and x has to go down to -1.
4) Connect the dots.
Draw a line between (0,1) and (-1,0).
Draw a line between (0,9) and (3,0).
 
 
Hi again L;
y = x + 1
y = -3x + 9
Both equations are in SLOPE-INTERCEPT FORMAT...
y=mx+b
m is the slope.
b is the y-intercept, the value of y when x=0.
FIRST EQUATION...
y = x + 1
Slope, m, is 1.
Y-intercept, b, is 1.
SECOND EQUATION...
y = -3x + 9
Slope, m, is -3.
Y-intercept, b, is 9.
It would be helpful to know at what point the two lines intersect.  Let's subtract the second equation from the first.  We could subtract the first equation from the second.  I randomly select this arrangement...
y = x + 1
-(y = -3x + 9)
0=4x-8
Let's subtract 4x from both sides...
-4x+0=4x-4x-8
-4x=-8
x=2
Let's plug-in x into either equation to solve for y.  I randomly select the first...
y = x + 1
y=2+1
y=3
Let's check our results with the second equation...
y = -3x + 9
3=[(-3)(2)]+9
3=-6+9
3=3
The lines intersect at coordinate (2,3).