Question

Solve system of equations
Y=x+z+5
Z=-3y-3
2x-y=-4

Answer 1

To begin, we will solve the third equation for x:

2x - y = -4

2x = y - 4

x = (y - 4)/2

Substituting this value of x into the first equation:

Y = x + z + 5

Y = ((y - 4)/2) + z + 5

Y = (y/2) + (z/2) + (5/2) - 2

Next, we can substitute the second equation (-3y - 3) for z in terms of y:

Z = -3y - 3

Now, we have expressed Y and Z in terms of y. We can substitute these expressions into the first equation:

(Y) = ((y/2) + (z/2) + (5/2) - 2)

Simplifying this expression:

Y = (y/2) + (z/2) + (5/2) - 2

Y = (y/2) + (-3y - 3)/2 + (5/2) - 2

Y = (y - 3y - 3 + 5 - 4)/2

Y = (-2y - 2)/2

Y = -y - 1

Thus, the solution to the system of equations is:

X = (y - 4)/2

Y = -y - 1

Z = -3y - 3