3-4 Systems of Equations in Three Variables Solve each system of equations. 15. SOLUTION:
Eliminate one variable. Multiply the first and second equation by 3 and 5 respectively then add.
Multiply the second equation by 2 and add with the third equation.
Solve the fourth and fifth equations.
Substitute –4 for x in the fifth equation and solve for z.
Substitute –4 and 6 for x and z in the first equation and solve for y.
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Therefore, the solution is (–4, –1, 6).
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3-4 Systems of Equations in Three Variables
Therefore, the solution is (–4, –1, 6).
17. SOLUTION:
Eliminate one variable. Multiply the first equation by 4 and add with the second equation.
Multiply the first equation by 7 and add with the third equation.
Solve the fourth and the fifth equation.
This is a false statement. Therefore, there is no solution.
19. SOLUTION:
Eliminate one variable. Multiply the first equation by –3 and add with the second equation.
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3-4 Systems of Equations in Three Variables This is a false statement. Therefore, there is no solution.
19. SOLUTION:
Eliminate one variable. Multiply the first equation by –3 and add with the second equation.
Multiply the second equation by –4 and add with the third equation.
Multiply the second equation by –4 and the third equation by 3 then add.
Since the equations 4, 5 and 6 are same, the system has an infinite number of solutions. 23. FINANCIAL LITERACY Kate invested $100,000 in three different accounts. If she invested $30,000 more in account A than account C and is expected to earn $6300 in interest, how much did she invest in each account?
SOLUTION: Let a, b and c be the amount invested in the Account A, B and C respectively.
Kate invested $30,000 more in account A than account C. eSolutions Manual - Powered by Cognero
Therefore,
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SOLUTION: Let a, b and c be the amount invested in the Account A, B and C respectively.
3-4 Systems of Equations in Three Variables
Kate invested $30,000 more in account A than account C.
Therefore,
Substitute c + 30000 for a in the first equation and simplify.
Total interest amount is $6300. That is,
.
Substitute c + 30000 for a and simplify.
Solve the third and fourth equations.
Substitute 25000 for c in the second equation and solve for a.
Substitute 25000 for c in the third equation and solve for b.
Therefore, she invested $55,000, $20,000 and $25,000 in the account A, B and C respectively.
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