Question 59409
Here's an example of a problem that I solved for another student, I explained the steps.  I hope that makes things clearer.
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Solve the following systems by addition. If a unique solution does not exist, I need to state whether the system is inconsistent or dependent.
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L1) 2x + 3y = 1
L2) 5x + 3y = 16
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Multiply L2 by -1 and add it to L2 and the y's will be eliminated.
-1(5x+3y)=-1(16) --->> -5x-3y=-16
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2x +3y=1
-5x-3y=-16
____________
-3x+0y=-15
-3x=-15
-3x/-3=-15/-3
x=5
Substitute x=5 into L1 and solve for y:
2(5)+3y=1
10+3y=1
-10+10+3y=1-10
3y=-9
3y/3=-9/3
y=-3
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The solution is (x,y)=(5,-3)
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FYI, if you go to eliminate one variable and both variables get eliminated and you get two numbers that aren't equal like 4=5, then the system has no solution and is inconsistent. If the same thing happens, but the numbers left do equal each other like 4=4, then the system has an infinite number of solutions and the system is dependent.
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Happy Calculating!!!