Question

Use back-substitution to solve the system. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set z = t and solve for x and y in terms of t.) −x + y − z = 0 2y + z = 7 1 2 z = 0 (x, y, z) =____________

Answer 1

Explanation:

Given the system of equations

−x + y − z = 0 ......... 1

2y + z = 7 .......... 2

1/2 z = 0 .......... 3

To solve the system of equations, we will have to set z= t since the equation has infinite number of solutions.

Next is to write the other variables x and y in terms of t.

Substitute z = t into equation 2 as shown;

From equation2; 2y + z = 7

2y + t = 7

subtract t from both sides;

2y + t - t= 7-t

2y = 7-t

divide both sides by 2;

2y/2 = 7-t/2

y = (7-t)/2

Substitute z = t and y = (7-t)/2 into equation 1;

From equation 1; −x + y − z = 0

-x+(7-t)/2-t = 0

-x = t-(7-t)/2

-x = [2t-(7-t)]/2

-x = 2t-7+t/2

-x = 3t-7/2

x = (7-3t)/2

Hence (x, y, z) =((7-3t)/2, (7-t)/2, t)