Question 471560
Use back-substitution to solve the triangular system.
{ x+y-3z=7
{ y-3z=4
{z=-5
solve for ( x, y , z ) =

In this problem, it is asking us to find the value of x, y, and z. TO do this, we simply need to re- read the problem. In the problem, z is given to us as -5, so we would state that z=-5. From there,we substitute -5 for z. So, the equation y-3z=4 would be rewritten as y-3(-5)=4. We then multiply -3 by -5 to get 15. Then, we subtract both sides of the equation by 15. Then, we see that y=-11.

Here is the problem step by step.

1. y-3z=4  Rewrite the original problem.
2. y-3(-5) Substitute the given -5 for z.
3. y+15=4  Multiply -3 by -5. Remember that a negative (-) multiplied by another negative (-) equals a positive (+)
4. y=-11.  Subtract 15 from both sides of the equation.

Now, to find the value of x, we use the information we just found and the given value of z and substitute appropriately. I will solve below step by step.

1. x+y-3z=7 Rewrite the original problem.
2. x+(-11)+3(-5)=7 Substitute where values are known.
3. x+(-11)-15=7  Multiply 3 and -15
4. x-11-15=7  Distribute a positive 1 through the parentheses. In other words, multiply -11 by 1. Remember that a positive (+) multiplied by a negative (-) is equal to a negative number.
5. x-26=7  Add -11 to -15.
6. x=33  Add 26 to both sides of the equation.

Finally, we see that all equations have been solved and we know the values of the variables.
x=33 y=-11 z=-5

Hope this is what you needed.
Ashley