Question

2x - 3y = 9; 2x + y = 13

Answer 1

Answer:

See explanations below

Step-by-step explanation:

Given the simultaneous equations;

2x - 3y = 9... 1

2x + y = 13 ... 2

From 2;

y = 13-2x

Substitute into 1;

2x - 3(13-2x) = 9

2x -39 + 6x = 9

8x - 39 = 9

8x = 9+39

8x = 48

x = 6

Since y  = 13-2x

y = 13-2(6)

y = 13-12

y = 1

The soluton to the system of equation is (6, 1)

Given the equations;

99x + 101y = 499; .... 1 * 101

101x + 99 y = 501 ... 2 * 99

______________

9999x + 10,201y = 50,399

9999x + 9801y = 49,599

Subtract

10201y - 9801y = 50399-49599

400y = 800

y = 2

Substitute y = 2 into 1;

From 1;

99x + 101y = 499

99x + 101(2) =499

99x +202 = 499

99x = 499 - 202

99x = 198

x = 198/99

x =2

Hence the solution is (2,2)

For the equations;

49x - 57y = 172 .... * 57

57x - 49y = 252 __ * 49

____________________

2793x -3249y =  9804

2793x - 2401y = 12348

Subtract

-3249y+2401y = 9804-12348

-848y = -2544

y = 3

Substitute into 1;

49x - 57y = 172

49x - 57(3) = 172

49x - 171 = 172

49x = 171+172

49x = 343

x = 7

Hence the solution is (7, 3)