6-3 Elimination Using Addition and Subtraction Use elimination to solve each system of equations. 7. −v + w = 7 v+w=1 SOLUTION: Because −v and v have opposite coefficients, add the equations.
Now, substitute 4 for w in either equation to find the value of v.
The solution is (−3, 4). Check the solution in each equation.
8. y + z = 4 y −z = 8 SOLUTION: Because z and −z have opposite coefficients, add the equations.
Now, substitute 6 for y in either equation to find the value of z.
The solution is (6, −2).
Check the solution in each equation.
8. y + z = 4 y −z = 8 SOLUTION: Because z and −z have opposite coefficients, add the equations.
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9. −4x + 5y = 17 4x + 6y = −6 SOLUTION: Because 4x and −4x have opposite coefficients, add the equations.
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6-3 Elimination Using Addition and Subtraction 9. −4x + 5y = 17 4x + 6y = −6 SOLUTION: Because 4x and −4x have opposite coefficients, add the equations.
Now, substitute 1 for y in either equation to find the value of x.
10. 5m − 2p = 24 3m + 2p = 24 SOLUTION: Because 2p and −2p have opposite coefficients, add the equations.
Now, substitute 6 for m in either equation to find the value of p .
The solution is (−3, 1). Check the solution in each equation.
The solution is (6, 3). Check the solution in each equation.
10. 5m − 2p = 24 3m + 2p = 24 SOLUTION: Because 2p and −2p have opposite coefficients, add the equations. eSolutions Manual - Powered by Cognero
11. a + 4b = −4 a + 10b = −16 SOLUTION: Because a and a have the same coefficients, subtract the equations.
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6-3 Elimination Using Addition and Subtraction 11. a + 4b = −4 a + 10b = −16 SOLUTION: Because a and a have the same coefficients, subtract the equations.
12. 6r − 6t = 6 3r − 6t = 15 SOLUTION: Because −6t and −6t have the same coefficients, multiply equation 2 by –1 and then add the equations to solve for r.
Now, substitute −2 for b in either equation to find the value of a. Now, substitute −3 for r in either equation to find the value of t. The solution is (4, −2). Check the solution in each equation.
The solution is (−3, −4). Check the solution in each equation.
12. 6r − 6t = 6 3r − 6t = 15
SOLUTION: Because −6t and −6t have the same coefficients, multiply equation 2 by –1 and then add the equations to solve for r. eSolutions Manual - Powered by Cognero
13. 6c − 9d = 111 5c − 9d = 103 SOLUTION:
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6-3 Elimination Using Addition and Subtraction 13. 6c − 9d = 111 5c − 9d = 103
14. 11f + 14g = 13 11f + 10g = 25
SOLUTION: Because −9d and −9d have the same coefficients, subtract the equations.
SOLUTION: Because 11f and 11f have the same coefficients, you can multiply equation 2 by −1, then add the equations to find g.
Now, substitute 8 for c in either equation to find the value of d.
Now, substitute −3 for g in either equation to find the value of f . The solution is (8, −7). Check the solution in each equation.
The solution is (5, −3). Check the solution in each each equation.
14. 11f + 14g = 13 11f + 10g = 25
SOLUTION: Because 11f and 11f have the same coefficients, you can multiply equation 2 by −1, then add the equations to find g. eSolutions Manual - Powered by Cognero
15. 9x + 6y = 78 3x − 6y = −30 SOLUTION:
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6-3 Elimination Using Addition and Subtraction 15. 9x + 6y = 78 3x − 6y = −30 SOLUTION: Because 6y and −6y have opposite coefficients, add the equations.
Now, substitute 4 for x in either equation to find the value of y.
The solution is (4, 7). Check the solution in each equation.
16. 3j + 4k = 23.5 8j − 4k = 4 SOLUTION: Because 4k and −4k have opposite coefficients, add the equations.
Now, substitute 2.5 for j in either equation to find the value of k .
The solution is (2.5, 4). Check the solution in both equations.
16. 3j + 4k = 23.5 8j − 4k = 4 SOLUTION: Because 4k and −4k have opposite coefficients, add eSolutions Manual - Powered by Cognero the equations.
17. −3x − 8y = −24 3x − 5y = 4.5 SOLUTION: Because −3x and 3x have opposite coefficients, add the equations. Page 5
6-3 Elimination Using Addition and Subtraction 17. −3x − 8y = −24 3x − 5y = 4.5
18. 6x − 2y = 1 10x − 2y = 5
SOLUTION: Because −3x and 3x have opposite coefficients, add the equations.
SOLUTION: Because −2y and −2y have the same coefficients, subtract the equations.
Now, substitute 1.5 for y in either equation to find the value of x.
Now, substitute 1 for x in either equation to find the value of y.
The solution is (4, 1.5). Check the solution in each equation.
The solution is (1, 2.5). Check the solution in each equation.
18. 6x − 2y = 1 10x − 2y = 5 SOLUTION: Because −2y and −2y have the same coefficients, subtract the equations. eSolutions Manual - Powered by Cognero
Use elimination to solve each system of equations. 24. 4(x + 2y) = 8 4x + 4y = 12 SOLUTION: Distribute the 4 in the first equation.
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6-3 Elimination Using Addition and Subtraction Use elimination to solve each system of equations. 24. 4(x + 2y) = 8 4x + 4y = 12
The solution is (4, −1). 25. 3x − 5y = 11 5(x + y) = 5 SOLUTION: Distribute the 5 in the second equation.
SOLUTION: Distribute the 4 in the first equation.
Because −5y and 5y have opposite coefficients, add the equations.
Because 4x and 4x have the same coefficients, subtract the equations.
Now, substitute 2 for x in either equation to find the value of y.
Now, substitute −1 for y in either equation to find the value of x.
The solution is (2, −1).
The solution is (4, −1). 25. 3x − 5y = 11 5(x + y) = 5 SOLUTION: Distribute the 5 in the second equation.
26. 4x + 3y = 6 3x + 3y = 7 SOLUTION: Because 3y and 3y have the same coefficients, multiply equation 2 by −1, and add the equations to find x..
Because −5y and 5y have opposite coefficients, add the equations.
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6-3 Elimination Using Addition and Subtraction
The solution is
The solution is (2, −1).
.
27. 6x − 7y = −26 6x + 5y = 10
26. 4x + 3y = 6 3x + 3y = 7 SOLUTION: Because 3y and 3y have the same coefficients, multiply equation 2 by −1, and add the equations to find x..
SOLUTION: Because 6x and 6x have the same coefficients, subtract the equations.
Now, substitute 3 for y in either equation to find the value of x.
Now, substitute −1 for x in either equation to find the value of y.
The solution is
.
28. The solution is
. SOLUTION:
27. 6x − 7y = −26 6x + 5y = 10 SOLUTION: Because 6x and 6x have the same coefficients, subtract the equations.
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Because
y and − y have the same coefficients,
add the equations.
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Now, substitute 12 for x in either equation to find the
The solution is
6-3 Elimination Using Addition and Subtraction The solution is .
28.
.
29.
SOLUTION: Because
SOLUTION:
y and − y have the same coefficients,
add the equations.
Because
x and − x have opposite coefficients,
add the equations.
Now, substitute 12 for x in either equation to find the value of y.
Now, substitute
for y in either equation to find
the value of x.
The solution is
.
29.
The solution is
.
SOLUTION: eSolutions Manual - Powered Because x and −by Cognero x have opposite
add the equations.
coefficients,
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