Question

205 Solve the following simultaneous equations
© 2x + y = 5: 3x - y = 5
(iii) x+y=11: 2x - 3y = 7
2x - y = 5: 3x + 2y = 11​

Answer 1

Step-by-step explanation:

1. 2x + y = 5...................1

+ 3x - y = 5.....................2

______________________

5x =10 addition

x=10/5

x=2

put x=2 in eq 1

2x + y = 5

2×2+y=5

4+y=5

y=5-4

y=1

(x,y)=(2,1) is a solution of equation.

(ii) x+y=11: 2x - 3y = 7

x+y=11...............1

2x - 3y = 7..............2

multiplying eq 1 with 3 and 2 with 1

3x+3y=33.................3

+ 2x-3y=7........................4

____________________

5x=26

x=26/5

put x=26/5 in eq 1

x+y=11

26+y=11

5

multiply both sides by 5

26+5y=55

5y=55-26

5y=29

y=29/5

(x,y)=(26/5,29/5) is a solution of equation.

3.2x - y = 5: 3x + 2y = 11

2x - y = 5...............1

3x + 2y = 11...........2

multiplying eq 1 with 2 and 2 with 1

4x - 2y = 10.............3

+ 3x + 2y = 11...........4

____________________

7x=21

x=21/7

x=3

put x=3 in eq 1

2x-y=5

2×3-y=5

6-y=5

-y=5-6

-y=-1

y=1

(x,y)=(3,1) is a solution of equation.