[addition method][section 25]

(1.) 2x + y = 7

3x - y = 3 here is the problem
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5x = 10 add equations
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5 5 divide each side by 5

x = 2 divide and cancel

2(2) + y = 7 replace x with 2

4 + y = 7 multiply

-4 -4 subtract 4 from each side
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y = 3 subtract

result: x = 2 and y = 3

(2.) a + 5b = 10

-a + 4b = 8 here is the problem
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9b = 18 add equations
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9 9 divide each side by 9

b = 2 divide and cancel

a + 5(2) = 10 replace b with 2

a + 10 = 10 multiply

-10 -10 subtract 10 from each side
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a = 0 subtract

result: a = 0 and b = 2

(3.) 7x + 3y = 19

4x - 3y = 3 here is the problem
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11x = 22 add equations
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11 11 divide each side by 11

x = 2 divide and cancel

7(2) + 3y = 19 replace x with 2

14 + 3y = 19 multiply

-14 -14 subtract 14 from each side
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3y = 5 subtract
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3 3 divide each side by 3

y = 5/3 cancel

result: x = 2 and y = 5/3

(4.) -7c - 8d = 8

7c - 8d = 8 here is the problem
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-16d = 16 add equations
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-16 -16 divide each side by -16

d = -2 divide and cancel

7c - 8(-2) = 8 replace d with -2

7c + 16 = 8 multiply

-16 -16 subtract 16 from each side
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7c = -8 subtract
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7 7 divide each side by 7

c = -8/7 cancel

result: c = -8/7 and d = -2

(5.) x + 3y = 9

-x + 2y = 6 here is the problem
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5y = 15 add equations
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5 5 divide each side by 5

y = 3 divide and cancel

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

x + 9 = 9 multiply

-9 -9 subtract 9 from each side
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x = 0 subtract

result: x = 0 and y = 3

(6.) (3/4)x - (1/2)y = 4

(1/4)x + (1/2)y = 2.5 here is the problem
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x = 6.5 add equations

(1/4)(6.5) + (1/2)y = 2.5 replace x with 6.5

1.625 + (1/2)y = 2.5 multiply

- 1.625 - 1.625 subtract 1.625 from
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(1/2)y = 0.875 subtract

2(1/2)y = (2)(0.875) multiply each side by 2

y = 1.75 multiply

result: x = 6.5 and y = 1.75

(7.) (1/2)x + y = 9

(3/4)x - y = 0 here is the problem
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1.25x = 9 add equations
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1.25 1.25 divide each side by 1.25

x = 7.2 divide and cancel

(1/2)(7.2) + y = 9 replace x with 7.2

3.6 + y = 9 multiply

-3.6 -3.6 subtract 3.6 from each side
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y = 5.4 subtract

result: x = 7.2 and y = 5.4

(8.) 0.4x + y = 1.2

0.6x - y = 3.9 here is the problem
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x = 5.1 add equations

0.4(5.1) + y = 1.2 replace x with 5.1

2.04 + y = 1.2 multiply

-2.04 - 2.04 subtract 2.04 from each side
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y = -0.84 subtract

result: x = 5.1 and y = -0.84

(9.) 2x - 3y = 8

2x + 3y = 4 here is the problem
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4x = 12 add equations
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4 4 divide each side by 4

x = 3 divide and cancel

2(3) + 3y = 4 replace x with 3

6 + 3y = 4 multiply

-6 -6 subtract 6 from each side
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3y = -2 subtract
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3 3 divide each side by 3

y = -2/3 cancel

result: x = 3 and y = -2/3

(10.) 7a + 6b = 0

15a - 6b = 0 here is the problem
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22a = 0 add equations
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22 22 divide each side by 22

a = 0 divide and cancel

7(0) + 6b = 0 replace a with 0

6b = 0 multiply and add
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6 6 divide each side by 6

b = 0 divide and cancel

result: a = 0 and b = 0