[elimination method][section 26]

(1.) 3x + y = 9 here is the problem

2x + y = 1

3x + y = 9 put this here

-2x - y = -1 multiply equation 1 thru by -1
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x = 8 subtract equations

3(8) + y = 9 replace x with 8

24 + y = 9 multiply

-24 -24 subtract 24 from each side
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y = -15 subtract

result: x = 8 and y = -15

(2.) 5r - s = -23

3r - s = -15 here is the problem

5r - s = -23 put this here

-3r + s = 15 multiply equation 2 thru by -1
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2r = -8 add equations
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2 2 divide each side by 2

r = -4 divide and cancel

3(-4) - s = -15 replace r with -4

-12 - s = -15 multiply

12 + s = 15 multiply thru by -1

-12 -12 subtract 12 from each side
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s = 3 subtract

result: r = -4 and s = 3

(3.) 2x + 3y = 8

3x + y = 5 here is the problem

9x + 3y = 15 multiply equation 2 thru by 3

-2x - 3y = -8 multiply equation 1 thru by -1
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7x = 7 subtract equations
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7 7 divide each side by 7

x = 1 divide and cancel

3(1) + y = 5 replace x with 1

3 + y = 5 multiply

-3 -3 subtract 3 from each side
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y = 2 subtract

result: x = 1 and y = 2

(4.) 2x + y = 3

7x - 4y = 18 here is the problem

8x + 4y = 12 multiply equation 1 thru by 4
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15x = 30 add equations
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15 15 divide each side by 15

x = 2 divide and cancel

2(2) + y = 3 replace x with 2

4 + y = 3 multiply

-4 -4 subtract 4 from each side
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y = -1 subtract

result: x = 2 and y = -1

(5.) 5x + y = 15

3x + 2y = 9 here is the problem

10x + 2y = 30 multiply equation 1 thru by 2

-3x - 2y = -9 multiply equation 2 thru by -1
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7x = 21 subtract equations
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7 7 divide each side by 7

x = 3 divide and cancel

5(3) + y = 15 replace x with 3

15 + y = 15 multiply

-15 -15 subtract 15 from each side
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y = 0 subtract

result: x = 3 and y = 0

(6.) 7r - 5t = -2

-8r - t = 9 here is the problem

40r + 5t = -45 multiply equation 2 thru by -5

7r - 5t = -2 put this here
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47r = -47 add equations
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47 47 divide each side by 47

r = -1 divide and cancel

-8(-1) - t = 9 replace r with -1

8 - t = 9 multiply

-8 + t = -9 multiply thru by -1

+ 8 +8 add 8 to each side
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t = -1 add

result: r = -1 and t = -1

(7.) 4p - 2q = 20

p + 5q = -17 here is the problem

-4p - 20q = 68 multiply equation 2 thru by -4

4p - 2q = 20 put this here
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-22q = 88 add equations
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-22 -22 divide each side by -22

q = -4 divide and cancel

p + 5(-4) = -17 replace q with -4

p - 20 = -17 multiply

+ 20 + 20 add 20 to each side
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p = 3 add

result: p = 3 and q = -4

(8.) 2a + 5b = 18

-5a + b = -18 here is the problem

25a - 5b = 90 multiply equation 2 thru by -5

2a + 5b = 18 put this here
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27a = 108 add equations
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27 27 divide each side by 27

a = 4 divide and cancel

2(4) + 5b = 18 replace a with 4

8 + 5b = 18 multiply

-8 -8 subtract 8 from each side
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5b = 10 subtract
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5 5 divide each side by 5

b = 2 divide and cancel

result: a = 4 and b = 2


(9.) 2u + 2z = 8

5u - 3z = 4 here is the problem

6u + 6z = 24 multiply equation 1 thru by 3

10u - 6z = 8 multiply equation 2 thru by 2
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16u = 32 add equations
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16 16 divide each side by 16

u = 2 divide and cancel

2(2) + 2z = 8 replace u with 2

4 + 2z = 8 multiply

-4 -4 subtract 4 from each side
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2z = 4 subtract
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2 2 divide each side by 2

z = 2 divide and cancel

result: u = 2 and z = 2

(10.) 4a + 3b = -2

8a - 2b = 12 here is the problem

-8a - 6b = 4 multiply equation 1 thru by -2
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-8b = 16 add equations
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-8 -8 divide each side by -8

b = -2 divide and cancel

4a + 3(-2) = -2 replace b with -2

4a - 6 = -2 multiply

+ 6 +6 add 6 to each side
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4a = 4 add
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4 4 divide each side by 4

a = 1 divide and cancel

result: a = 1 and b = -2