Question 58035This question is from textbook Beginning Algebra
: Can someone help me on ths problem?
I need to solve the following systems by addition. If a unique solution does not exist, I need to state whether the system is inconsistent or dependent.
2x + 3y = 1
5x + 3y = 16
Thanks so much,
Sher
This question is from textbook Beginning Algebra
Found 2 solutions by stanbon, funmath:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I need to solve the following systems by addition. If a unique solution does not exist, I need to state whether the system is inconsistent or dependent.
1st: 2x + 3y = 1
2nd: 5x + 3y = 16
Subtract 1st from 2nd to get:
3x=15
x=5
Substitute in 1st or in 2nd to solve for y.
2(5)+3y=1
10+3y=1
3y=-9
y=-3
Solution:
x=5, y=-3
Cheers,
Stan H.
Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website! Hi Sher,
I need to solve the following systems by addition. If a unique solution does not exist, I need to state whether the system is inconsistent or dependent.
:
L1) 2x + 3y = 1
L2) 5x + 3y = 16
:
Multiply L2 by -1 and add it to L2 and the y's will be eliminated.
-1(5x+3y)=-1(16) --->> -5x-3y=-16
:
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
:
The solution is (x,y)=(5,-3)
:
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.
:
Happy Calculating, Sher.
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