Question

Solve the system by substitution. Write the ordered triple in terms of y.

x−2y−z=1
2x−y−5z=5
y−z=1

Answer 1

To solve the given system by substitution, we expressed z in terms of y from the third equation and then solved the other equations for x and y, eventually finding the ordered triple (10, 4, 3).

Step-by-step explanation:

To solve the system by substitution and write the ordered triple in terms of y, we must first solve one of the equations for one variable and substitute it into the other equations.

From the given system:

• x - 2y - z = 1
• 2x - y - 5z = 5
• y - z = 1

We can express z in terms of y from the third equation: z = y - 1. Substitute z into the other two equations:

1. x - 2y - (y - 1) = 1 solve for x
2. 2x - y - 5(y - 1) = 5

From (1) we get x = 3y - 2. Now substitute x and z into (2):

1. 2(3y - 2) - y - 5(y - 1) = 5

Simplify and solve for y:

6y - 4 - y - 5y + 5 = 5
y = 4

Now back-substitute y = 4 into the expressions for x and z:

• x = 3(4) - 2 = 10
• z = 4 - 1 = 3

The ordered triple as a function of y is (10, 4, 3).