# Solve the following simultaneous equations.i. 2x + y = 5; 3x - y = 5ii. x - 2y = -1; 2x - y = 7iii. x + y = 11; 2x - 3y = 7iv. 2x + y = -2; 3x - y = 7v. 2x - y = 5; 3x + 2y = 11vi. x - 2y = -2; x + 2y = 10

(i)

2x + y = 5

y = 5 - 2x eq.[1]

3x - y = 5

Using eq.[1] we have

3x - (5 - 2x) = 5

3x - 5 + 2x = 5

5x = 10

x = 2

Using 'x' in eq.[1]

y = 5 - 2(2)

y = 5 - 4 = 1 cm

(ii)

x - 2y = -1

x = 2y - 1 eq.[1]

2x - y = 7

Using eq.[1], we have

2(2y - 1) - y = 7

4y - 2 - y = 7

3y = 9

y = 3

Using this value in eq.[1]

x = 2(3) - 1

x = 5

(iii)

x + y = 11

y = 11 - x eq.[1]

2x - 3y = 7

Using eq.[1], we have

2x - 3(11 - x) = 7

2x - 33 + 3x = 7

5x = 40

x = 8

Using this in eq.[1]

y = 11 - 8

y = 3

(iv)

2x + y = -2

y = -2x - 2 eq.[1]

3x - y = 7

Using eq.[1]

3x - (-2x - 2) = 7

3x + 2x + 2 =7

5x = 5

x = 1

Using this in eq.[1]

y = -2(1) - 2

y = -2 - 2 = -4

(v)

2x - y = 5

y = 2x - 5 eq.[1]

3x + 2y = 11

Using eq.[1]

3x + 2(2x - 5) = 11

3x + 4x - 10 = 11

7x = 21

x = 3

Using this in eq.[1]

y = 2(3) - 5

y = 1

(vi)

x - 2y = -2

x = 2y - 2 eq.[1]

x + 2y = 10

using eq.[1], we have

2y - 2 + 2y = 10

4y = 12

y = 3

Using this in eq.[1]

x = 2(3) - 2

x = 4

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