Question 65559: Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
x +5y = 10
-2x – 10y = -20
Solve each of the following problems. Be sure to show the equations used for the solution.
Number problems. Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?
Business and finance. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 Lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
1st: x +5y = 10
2nd: -2x – 10y = -20
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Let's say you choose to eliminate the x-terms by adding.
Since the coefficient of the 2nd equation is -2x you want
to create +2x in the 1st equation; so you multiply both
sides of the 1st equation by 2 as follows:
2(x+5y)=2(10)
3rd: 2x+10y=20
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Then you add the 2nd and 3rd equations to get:
0=0
This means equation #2 says the same thing as equation #3.
The system is dependent.
This means the two equations are really the same.
It also means that every point in the line x+5y=10 is a solution
point for the system of equations.
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Solve each of the following problems. Be sure to show the equations used for the solution.
Number problems. Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?
Let number of nickels be "x"; Value of these is 10x cents
Number of dimes is "50-x"; Value of these is 10(50-x)=(500-10x)cents
EQUATION:
value + value= 350cents
10x+500-10x=350
0=-150
This is a contradiction.
The system is inconsistent
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Business and finance. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 Lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?
Amount of $9 is "x" lbs; Value is 9x dollars
Amount of $12 is "100-x"; Value is 12(100-x)=1200-12x dollars
Amount of mixture is 100 lb; Value is 11.25(100)=1125 dollars
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EQUATION:
value + value = 1125 dollars
9x+1200-12x=1125
-3x=-75
x=25 lb (amount of $9 coffee)
100-x=75 lb (amount of $12 coffee)
Cheers,
Stan H.
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