Solve the system of equations: {3x - 6y + z = 0 -x + y - z = -1 x - 2y = -1 solv
ID: 3031911 • Letter: S
Question
Solve the system of equations: {3x - 6y + z = 0 -x + y - z = -1 x - 2y = -1 solve the system of equation {2x - 5y + z = -8 -x + y - z = 1 x - 3y = -6 Maricopa's Success scholarship fund receives a gift of $ 130000. The money is invested in stocks, bonds. and CDs. CDs pay 4.75 % interest, bonds pay 4.4 % interest, and stocks pay 6.8 % interest. Maricopa Success invests S 50000 more in bonds than in CDs. If the annual income from the investments is $ 6750, how much was invested in each account? Maricopa Success invested Maricopa Success invested Maricopa Success investedExplanation / Answer
8)
3x - 6y + z = 0 (1)
-x + y - z = -1 (2)
x - 2y = -1 (3)
we have 3 variables "x" , "y" and "z".
we can see that equation (3) has only 2 variables
so we try to remove the third variable from equation (1) and (2)
Adding equation (1) and (2) we get // by adding these two eq we can remove "z"
3x - 6y + z = 0
-x + y -z = -1
=>
2x - 5y = -1 (4)
now from (3) and (4)
multiplying eq (3) with "2"
we get
2x - 4y = -2 (5)
subtracting eq (5) and eq (4)
2x - 5y = -1
2x - 4y = -2
- + + // on subtracting we change the sign
=>
-y = 1
we get
y = -1
now from equation (3) we can find the value of "x"
x - 2y = -1
x - 2 * (-1) = -1
x + 2 = -1
x = -3
now from equation (1)
3x - 6y + z = 0
3 * (-3) - 6 * (-1) + z = 0
-9 + 6 + z = 0
z = 3
.
9)
2x - 5y + z = -8 (1)
-x + y - z = 1 (2)
x - 3y = -6 (3)
adding eq (1) and (2) // we can eliminate "z"
2x - 5y + z = -8
-x + y - z = 1
we get
x - 4y = -7 (4)
subtracting eq (3) and (4)
x - 3y = -6
x - 4y = -7
- + +
y = 1
now from equation (3)
x - 3y = -6
x - 3 * (1) = - 6 // since y = 1
x - 3 = -6
we get
x = -3
now from equation (2)
-x + y - z = 1
- (-3) + (1) - z = 1
3 + 1 - z = 1
z = 3
.
10)
Total fund recieved = $ 130,000
This recieved money is invested in stocks , bonds and CDs
Let the amount spent in CDs be "x".
Investment in Bonds = "50000 + x" // the investment in Bonds is 50000 more then CDs
Investment in Stocks = Total Investment - (Investment in Bonds + Investment in Stocks)
= 130000 - (50000 + x + x)
= 130000 - 50000 - 2x
= 80000 - 2x
Annual Income from the Investment = $ 6750
Annual Income from the Investment = Income from CDs + Income from Bonds + Income from Stocks (1)
CDs pays 4.75 % interest
Bonds pays 4.4% interest
Stocks pays 6.8 % interest
Income from CDs = amount invested * Interest payed / 100
= x * 4.75 / 100 = > 4.75x/100
Income from Bonds = amount invested * Interest payed / 100
= ( 50000 + x) * 4.4 / 100
= 2200 + 4.4x/100
Income from Stocks = amount invested * Interest payed / 100
= ( 80000 - 2x ) * 6.8 / 100
= 5440 - 13.6x/100
now from eq (1)
6750 = 4.75x/100 + 2200 + 4.4x/100 + 5440 - 13.6x / 100
6750 = 4.75x/100 + 4.4x/100 -13.6x/100 + 7640
-890 = -4.45x/100
890 = 4.45x/100
x = 20000
So the amount invested in CDs = $ 20,000
Amount invested in Bonds = 50000 + x => 50000 + 20000 = $ 70,000
Amount Invested in Stocks = 80000 - 2x => 80000 - 2*(20000) => 80000 - 40000 = $ 40,000