Question

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Answer 1

1. a) {x + y = 2 {x = 2 - y

{3x + 2y = 3 {3x + 2y = 3

3(2- y) + 2y = 3

6 - 3y + 2y = 3

-y = 3- 6

-y = -3

y = 3

x = 2 - y = 2 - 3 = -1

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b) {-x + y = 4 {x = -4 + y

{5x + 2y = 8 {5x + 2y = 8

5(-4 + y) + 2y = 8

-20 + 7y = 8

7y = 8 + 20

7y = 28

y = 28 : 7 = 4

x = -4 + y = - 4 + 4 = 0

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c) {-3x + 4y = -6 {-3x + 4y = -6

{2x + y = 4 {y = 4 - 2x

-3x + 4 × (4 - 2x) = -6

-11x + 16 = - 6

-11x = - 6 - 16

-11x = - 22

x = - 22 : (-11) = 2

y = 4 - 2x = 4 - 2 × 2 = 4 - 4 = 0

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2. a) {x + y = 5 {x + y = 5

{x - y = 1 {x = 1 + y

1 + y + y = 5

1 + 2y = 5

2y = 5 - 1

2y = 4

y = 4 : 2 = 2

x = 1 + y = 1 + 2 = 3

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b) {x + y = 4 {y = 4 - x

{2x - y = -1 {2x - y = -1

2x - (4 - x) = - 1

3x - 4 = -1

3x = -1 + 4

3x = 3

x = 3 : 3 = 1

y = 4 - x = 4 - 1 = 3

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c) {x - y = -3 {x - y = -3

{3x + y = 11 {y = 11 - 3x

x - (11 - 3x) = -3

4x - 11 = -3

4x = - 3 + 11

4x = 8

x = 8 : 4 = 2

y = 11 - 3x = 11 - 3 × 4 = 11 - 6 = 5

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3. a) {x + 2y = -1 {2y = -1 - x

{4x - 2y = 6 {4x - 2y = 6

4x - (-1 - x) = 6

5x + 1 = 6

5x = 6 - 1

5x = 5

x = 5 : 5 = 1

4x - 2y = 6

4 × 1 - 2y = 6

-2y = 6 - 4

-2y = 2

y = 2 : (-2) = -1

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b) {3x + 4y = 6 {4y = 6 - 3x

{x - 4y = -14 {x - 4y = -14

x - (6 - 3x) = -14

4x - 6 = -14

4x = -14 + 6

4x = -8

x = -8 : 4 = -2

x - 4y = -14

-2 - 4y = -14

-4y = -14 + 2

-4y = - 12

y = -12 : (-4) = 3

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c) {4x + y = -5 {4x = -5 - y

{4x - 2y = -2 {4x - 2y = -2

-5 - y - 2y = -2

-3y = -2 + 5

-3y = 3

y = 3 : (-3) = -1

4x - 2y = -2

4x - 2 × (-1) = -2

4x + 2 = -2

4x = -2 - 2

4x = -4

x = -4 : 4 = -1