Question

solve the system education x-y=3,2x+3y+4z=17and y-2z=7​

Answer 1

Answer:

$the \: given \: equations \: are \\ 2x + 3y + 4z = 17.....(1) \\ x - y = 3.....(2) \\ y - 2z = 17....(3)$

$x = y + 3$

Now, convert equation 2 and 3 in terms of x and z respectively

$(2) - - > x = 3 +y \\ (3) - - > - 2z = 17 - y \\ z = - \frac{17 - y}{2}$

substituting the values of x and z in 1 we get,

$2(y + 3) + 3y + 4( - \frac{17 - y}{2}) = 17 \\ 5y + 6 - 2(17 - y) = 17 \\ 5y + 6 - 34 + 2y = 17 \\ 7y = 17 + 28 = 45 \\ y = \frac{45}{7}$

Now, substitute the value of y in 2 and 3

$x = 3 + \frac{45}{7} = \frac{21 + 45}{7} \\ x = \frac{66}{7} \\ z = \frac{ - 17 + \frac{45}{7} }{2} = \frac{ \frac{45 - 119}{7} }{2} \\ = - \frac{74}{2} \\ z = - 37$