Simple math Problems, please help!?

Question

1. Solve for X,Y,Z.

14X+6Y+2z=8
5X+0y+5Z-10=0

2. Solve for X and Y
Xsin35+ycos50=0
Ysin50+xcos35-10=0

Answer 1

1) The equations 14x + 6y + 2z = 8 and 5x + 0y + 5z - 10 = 0

14x + 6y + 2z = 8 ---> (1)

 5x + 5z = 10 ---> (2)

To solve the above system we need three equations to solving three variables.

 

2) The equations x sin35 + y cos50 = 0

y sin50 + x cos35 - 10 = 0

By using calculator we can able to write above equations,

0.57x +  0.64y = 0 ---> (1)

0.76y +  0.81x = 10 ---> (2)

Solve the equations by using elimination method.

0.76[0.57x +  0.64y = 0]

0.4332x + 0.4864y = 0 ---> (3)

- 0.64[y 0.76 + x 0.81 = 10]

-0.4864y - 0.5184 = - 6.4 --->(4)

To eliminate the y term, add (3) and (4) equations.

0.4332x + 0.4864y +( - 0.4864y - 0.5184) = 0 - 6.4

0.4332x + 0.4864y - 0.4864y - 0.5184 =  - 6.4

-0.0852x = - 6.4

x = 6.4/(0.0852)

x = 75.11

Substitute x = 75.11 in equation (1).

0.57(75.11) +  0.64y = 0

42.8127 + 0.64y = 0

0.64y = - 42.8127

y = - 66.89

Solution x = 75.11 and y = - 66.89.