The solution is (–2, 6).
6-4 Elimination Using Multiplication Use elimination to solve each system of equations. 7. x + y = 2 −3x + 4y = 15 SOLUTION: Notice that if you multiply the first equation by 3, the coefficients of the x–terms are additive inverses.
Now, substitute 3 for y in either equation to find x.
9. x + 5y = 17 −4x + 3y = 24 SOLUTION: Notice that if you multiply the first equation by 4, the coefficients of the x–terms are additive inverses.
Now, substitute 4 for y in either equation to find x.
The solution is (–3, 4).
The solution is (–1, 3).
10. 6x + y = −39 3x + 2y = −15
8. x − y = −8 7x + 5y = 16 SOLUTION: Notice that if you multiply the first equation by 5, the coefficients of the y–terms are additive inverses.
SOLUTION: Notice that if you multiply the first equation by –2, the coefficients of the y–terms are additive inverses.
Now, substitute –2 for x in either equation to find y.
Now, substitute –7 for x in either equation to find y.
The solution is (–7, 3). The solution is (–2, 6). 9. x + 5y = 17 −4x + 3y = 24 SOLUTION: Notice that if you multiply the first equation by 4, the coefficients of the x–terms are additive inverses.
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11. 2x + 5y = 11 4x + 3y = 1 SOLUTION: Notice that if you multiply the first equation by –2, the coefficients of the x–terms are additive inverses. Page 1
6-4 Elimination Using Multiplication The solution is (–7, 3). 11. 2x + 5y = 11 4x + 3y = 1
The solution is (0, 2). 13. 3x + 4y = 29 6x + 5y = 43
SOLUTION: Notice that if you multiply the first equation by –2, the coefficients of the x–terms are additive inverses.
SOLUTION: Notice that if you multiply the first equation by –2, the coefficients of the x–terms are additive inverses.
Now, substitute 3 for y in either equation to find x.
Now, substitute 5 for y in either equation to find x.
The solution is (–2, 3).
The solution is (3, 5).
12. 3x − 3y = −6 −5x + 6y = 12 SOLUTION: Notice that if you multiply the first equation by 2, the coefficients of the y–terms are additive inverses.
Now, substitute 0 for x in either equation to find y.
14. 8x + 3y = 4 −7x + 5y = −34 SOLUTION: Notice that if you multiply the first equation by 7 and the second equation by 8, the coefficients of the x– terms are additive inverses.
Now, substitute –4 for y in either equation to find x.
The solution is (0, 2). 13. 3x + 4y = 29 6x + 5y = 43 SOLUTION: Notice that if you multiply the first equation by –2, the coefficients of the x–terms are additive inverses.
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The solution is (2, –4). 15. 8x + 3y = −7 7x + 2y = −3
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SOLUTION: Notice that if you multiply the first equation by –2
6-4 Elimination Using Multiplication The solution is (2, –4). 15. 8x + 3y = −7 7x + 2y = −3
The solution is (1, –5). 16. 4x + 7y = −80 3x + 5y = −58
SOLUTION: Notice that if you multiply the first equation by –2 and the second equation by 3, the coefficients of the y–terms are additive inverses.
SOLUTION: Notice that if you multiply the first equation by –3 and the second equation by 4, the coefficients of the x–terms are additive inverses.
Now, substitute 1 for x in either equation to find y.
Now, substitute –8 for y in either equation to find x.
The solution is (1, –5). 16. 4x + 7y = −80 3x + 5y = −58 SOLUTION: Notice that if you multiply the first equation by –3 and the second equation by 4, the coefficients of the x–terms are additive inverses.
Now, substitute –8 for y in either equation to find x.
The solution is (–6, –8). 17. 12x − 3y = −3 6x + y = 1 SOLUTION: Notice that if you multiply the second equation by –2, the coefficients of the x–terms are additive inverses.
Now, substitute 1 for y in either equation to find x.
The solution is (0, 1). The solution is (–6, –8). eSolutions Manual - Powered by Cognero
17. 12x − 3y = −3 6x + y = 1
18. −4x + 2y = 0 10x + 3y = 8 SOLUTION: Page 3 Notice that if you multiply the first equation by –3 and multiply the second equation by 2, the
6-4 Elimination Using Multiplication The solution is (0, 1). 18. −4x + 2y = 0 10x + 3y = 8 SOLUTION: Notice that if you multiply the first equation by –3 and multiply the second equation by 2, the coefficients of the y–terms are additive inverses.
Now, substitute
for x in either equation to find y.
The solution is
.
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