Can someone please help!?!?

Question

1.) Solve the system analytically.

4x - 2y + 3z = 23
4x - 3y - 4z = -50

I get how to solve these systems with three equations, but not with two. The correct answer is {4, 10, 9}.

2.) Solve the system analytically.

x + z = 6
x + y = 5
y + z = 7

Correct answer is {2,3,4}, but how do you solve?

Answer 1

x + z  = 6    -(1)

x + y = 5     -(2)

y + z = 7     -(3)

Add the three equations and simplify we get

2(x + y + z) = 6 + 5 + 7

2(x + y + z) = 18

x + y + z = 9    -(4)

Substitute the equation (1) x + z = 6 in the equation (4)  x + y + z = 9

6 + y = 9

y = 3

Substitute the equation (2) x + y = 5 in the equation (4) x + y + z = 9

5 + z = 9

z = 4

Substitute the equation (3) y + z = 7 in the equation (4) x + y + z = 9

x + 7 = 9

x = 2

The answer is x = 2 , y = 3 and z = 4.

 

 

Answer 2

Three varaibles with two equations can not be solved and they can be expressed interms of other variable like

y = 28x /17 + 58/17

z = 169/17 - 4x /17