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Question 184483: 2. For the systems of linear equations in questions 1-3
- Determine how many solutions exist
- Use either elimination or substitution to find the solutions (if any)
- Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection
2x + 3y = 8 and 3x + 2y = 7
help is much appreciated!
G
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! The equations are 1st degree. That means there
are no powers higher than 1. Two 1st degree
equations can either:
(a) Be 2 parallel straight lines
(b) Be 2 straight lines that intersect at 1 point
(c) Be the same equation written twice
If there're parallel, they're lines with the
same slope, and have no solution. If they're
not parallel, they must have a solution
I'll put them in the form  , where
 = slope. If the slope is the same, there's
no solution
(1) 
(2) 
-----------------------
(1)
(1) 
(1) 
-----------------------
(2)
(2) 
(2) 
-----------------------
The slopes are not the same, so there is a solution
To solve, I'll multiply (1) by  and (2) by 
(1) 
(2) 
Now subtract (1) from (2)
(2)
(1) 
(3) 
(3) 
Put this back into either equation to find 
(1) 
(1) 
(1) 
This tells me that the point of intersection is (1,2)
Now I'll plot them
For each line, to find the x-intercept, set  and
solve for  . Then set  and solve for
for the y-intercept
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