solve the linear system of equations 3x 2y z 4 x 2y 3z

solve the linear system of equations 3x - 2y - z = -4 -x + 2y -3z = 18 -3x + y -z = 14 solve the system of equations: 4x - y = 1 x^2 + 2y = 7 For the information given, state the values of the trig functions of theta; tan theta = -5/6 and sin theta > 0

Solution

Here we first add first and third equation each side, so that x terms are deleted and we get

-2y+y-z-z= -4+14

or -y - 2z = 10

or y= -10-2z                   .............(iv)

Now we multiply second equation each side by 3 and subtract third equation from it as :

3(-x+2y-3z) - (-3x+y-z)= 18-14

or -3x+6y-9z +3x-y+z = 4

or 5y -8z = 4

or 5(-10-2z) -8z =4           (by (iv) equation)

or -50-10z -8z = 4

or -18z = 4- 50 = 4+50=54

z= - 54/18 = -3

so from (iv) equation

y= -10- 2z = -10 -2(-3) = -10+6= -4

and from first equation

3x-2(-4)-(-3) = -4

or 3x +8+3 = -4

or 3x = -4 -11 = -15

or x = -15/3= -5

so last answer is x= -5, y= -4 and z = -3

This is the answer of very first question.