Solve this problem

Question

Answer 1

First, let's add the bottom equation to the top equation so we can eliminate y and z to get x:

(x+y+z=5) + (3x-y-z=3) --> 4x=8 --> x=2

Now, plug x=2 into the second equation, which will be added to the bottom equation to eliminate z and get y:

(2-2y+z=8) + (3(2)-y-z=3) --> 8-3y=11 --> -3y=3 --> y=-1

Finally, use the top equation to plug in x=2 and y=-1 to get z:

x+y+z=5 --> 2+(-1)+z=5 --> 2-1+z=5 --> 1+z=5 --> z=4

Thus, the solution is (x,y,z) = (2,-1,4)

Hope this helped!

Answer 2

Given:

x + y + z = 5 (Eq. 1)

x - 2y + z = 8 (Eq. 2)

3x - y - z = 3 (Eq. 3)

A quick look at Eq. 1 & Eq. 3 reveals y & z both have their signs reversed (i.e.Eq. 1 has +y and +z whereas Eq. 3 has -y and -z). So we ADD these two equations

Adding Eq.1 & Eq.3, we get

4x = 8, therefore, x = 2

Similarly, Eq. 1 & Eq. 2 have x and z with same magnitude and same sign (+) in both equations. So we SUBTRACT the two equations

Eq.1 - Eq. 2 =>

3y = -3, therefore, y = -1

Substitute the values of x and y in any equation and get the value of z. I chose Eq.1, (x + y + z = 5)

2 -1 + z = 5, therefore, z= 4

Solution is (x:2,y:-1,z:4)