Systems Of Linear Equations

Systems of Linear Equations
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Systems of Linear Equations
The system has three variables if it has three quantities like X, Y, and Z. The quantities that applied in the equations can be utilized in real-life situations (Systems of linear equations in three variables, 2018).
1. Jane has a portfolio investment of $17,000 that she has decided to invest in three separate portfolios. The stakes are subdivided into savings, bonds and money markets each are resulting in annual interest payment to her. The stakes are; a savings account earning 6% in annual interest rate, a bond investment which at the end of the year attracts an interest of 9%, and a stake in the money markets that gives her a return of 11%. The annual interest, when totaled for both investments, results in a gain of $1540. Also, the amount that she has invested in bonds is three times more than the stake put savings account. Calculate the amount that Jane has invested in each of the accounts?
Solution
Savings = x
Bonds = y
Money markets = z
X + y + z = 17,000
0.06x + 0.09y +0.11y = 1540
-3x + y = 0
Step Two – Addition
X + y + z = 17,000 (o.11)
0.06x + 0.09y +0.11y = 1540
=
(0.11X + 0.11y + 0.11z = 1870)
–
(0.06x + 0.09y +0.11y = 1540) = 0.5x + 0.2y = 330
Step three – Addition
0.5x + 0.2y = 330
-3x + y = 0 (0.2)
= 0.5x + 0.2y = 330
-( -0.6x + 0.2y) = 0
= 0.11x = 330/0.11 = 33000/11 = 3000
X = 3000
Y = 9000- y = o
y= 9000
Z = 5000
2. A theatre sales adult tickets for $6 while those for students and children go for $3.

50 and $2.50 respectively. The theatre sold 278 tickets amounting to $1300 a single day. Calculate the tickets sold by the theatre among the three distinct groups if the sales for adults were 10 lesser than double that of students.
Step 1
X + y + z = 278
6x + 3.5Y + 2.5z = 1300
X – 2y = -10
Step 2 – Addition
2.5x + 2.5y + 2.5z = 695
-6x + 3.5y + 2.5z = 1300
= -3.5x – y = – 605
Step 3- Addition
-3.5x – y = – 605 (2)
X – 2y = – 10
= -7x – 2y = -1210
-(X – 2y = – 10)
= -8x= – 1200
X = 150
Y = 150 – 2y = -10
-160 = – 2y
Y = 80
Z = 150 – 80 – z = 278
Z = 48
References
Systems of Linear Equations in Three Variables. (2018). [eBook]. Retrieved from http://www.teaching.martahidegkuti.com/Math99/math99_fa16/3by3systems.pdf