SOLUTION: The sum of 3 numbers is 21. 3 times the first number increased by four times the second number plus the third number is 14. The sum of two times the first and seven times the secon

Question 1171788: The sum of 3 numbers is 21. 3 times the first number increased by four times the second number plus the third number is 14. The sum of two times the first and seven times the second number, increased by the third number is -18. If the first number is represented by x, the second number is represented by y, and the third number is represented by a, write a system of equation that could be used to solve for the variables.
Can someone give me step by step instructions on how to solve problems like this?
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of 3 numbers is 21. 3 times the first number increased by four times the second number plus the third number is 14. The sum of two times the first and seven times the second number, increased by the third number is -18. If the first number is represented by x, the second number is represented by y, and the third number is represented by a, write a system of equation that could be used to solve for the variables.
Can someone give me step by step instructions on how to solve problems like this?
:
Write an equation for each statement
:
The sum of 3 numbers is 21.
x + y + a = 21
3 times the first number increased by four times the second number plus the third number is 14.
3x + 4y + a = 14
The sum of two times the first and seven times the second number, increased by the third number is -18.
2x + 7y + a = -18
:
Use elimination on the 1st two equation
3x + 4y + a = 14
x + y + a = 21
------------------Subtraction eliminates a
2x + 3y = -7
:
Do the same on the 1st and 3rd equation
2x + 7y + a = -18
x + y + a = 21
-------------------
x + 6y = -39
;
Take the resulting equations, multiply the above by 2
2x + 12y = -78
2x + 3y = -7
----------------Subtraction eliminates x, find y
9y = -71
y = -71/9
y = -7.8888
At this point it is apparent that the solutions are not integers. which leads me to suspect there is a mistake in the problem.
Anyway, find x
x + 6(-7.888) = -39
x + -47.333 = - 39
x = -39 + 47.3333
x = 8.3333
Find a
8.333 - 7.888 + a = 21
.445 + a = 21
a = 21 -.445
a = 20.555
I confirmed these solutions using the matrix feature on my Calc

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
The sum of 3 numbers is 21. 3 times the first number increased by four times the second number plus the third number is 14. The sum of two times the first and seven times the second number, increased by the third number is -18. If the first number is represented by x, the second number is represented by y, and the third number is represented by a, write a system of equation that could be used to solve for the variables.
Can someone give me step by step instructions on how to solve problems like this?

As requested 1st, 2nd, and 3rd numbers are: x, y, and a, respectively
x + y + a = 21 <====== The sum of 3 numbers is 21.
3x + 4y + a = 14 <====== 3 times the first number increased by four times the second number plus the third number is 14
2x + 7y + a = - 18 <====== The sum of two times the first and seven times the second number, increased by the third number is -18.
That's the system of 3 equations that you requested.
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