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Question 184719: 2.
- 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
0.2x + 0.4y = 1.7 and 8.3x - 6.3y = -4.3
need help desperately! Thank you.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! - 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
0.2x + 0.4y = 1.7 and 8.3x - 6.3y = -4.3
:
get rid of the decimals, multiply both equations by 10, results
2x + 4y = 17
83x - 63y = -43
;
We will use elimination;
Multiply the 1st equation by 83 and the 2nd equation by 2:
166x + 332y = 1411
166x - 126y = -86
--------------------subtraction eliminates x, find y
458y = 1497
y =  ; approx 3.3 on the graph
Find x using eq: 2x + 4y = 17
2x + 4() = 17
2x +  = 17
2x = - + 17
2x = - + 
2x = 
x =  *
x =  ; approx 2.0 on the graph
:
solution: x = ; y = ; this the point of intersection
:
Put both equations in the slope intercept form
2x + 4y = 17
4y = -2x + 17
y =  x + 
y =  x +
Plot two points
x = 4; y = 2 (substituted 4 for x in the above equation and found y)
x = 0; y = ; (4.25) this is also the y intercept (when x=0)
Graph of this
calculate the x intercept (when y = 0)
x + = 0
x = -
Multiply both side by -2, results
x =  = 8 is the x intercept, confirmed on the graph
:
Do the same with the 2nd equation;
83x - 63y = -43
-63y = -83x - 43
63y = 83x + 43; multiplied by -1
y =  x + 
Plot two points
x = 0, y = ; approx .7 on the graph; this the y intercept
x = 4, y =  ; approx 6 on the graph
:
Add this to the above graph:
:
Calculate the x intercept of this equation:
x + = 0
x = -
Multiply both sides by 63
83x = 43
x =  ; approx -.5 on the graph, (the x intercept
Summarize
Eq1: x intercept = 8.5, y intercept = 4.25
Eq2: x intercept = , y intercept =
Point of intersection: x = ; y = (approx 2, 3.3 on the graph
;
:
This problems was very time consuming, please take time to study it and learn
what's happening here. Carl
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