Solve this system using substitution:

(1,-4,4)

Step-by-step explanation:

  (x, y, z) = (1, -4, 4)

Step-by-step explanation:

The first equation lets you write an expression for z that can be used in the other two:

  z = 5x +3y +11

After substitution, you have the two-equation, two-unknown system ...

  x +2y +3(5x +3y +11) = 5   ⇒   16x +11y = -28

  3x +2y -2(5x +3y +11) = -13   ⇒   -7x -4y = 9

Substitution at this point involves fractions, but can be done. We choose to write an expression for y using the second equation.

  y = (-7x -9)/4

Substituting into the first gives ...

  16x +11(-7x -9)/4 = -28

  -13/4x = -13/4 . . . . . . add 99/4 and collect terms

  x = 1 . . . . . . . . . . multiply by -4/13

  y = (-7(1) -9)/4 = -4 . . . . use the expression for y

  z = 5(1) +3(-4) +11 = 5 -12 +11 = 4 . . . . use the expression for z

The solution is (x, y, z) = (1, -4, 4).

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Additional comment

Attached is an example of finding the solution using substitution with a graphing calculator. We write a function for z in terms of x and y (using the first equation), then substitute that where z is found in remaining equations. This gives a 2-variable system whose solution can be used to find the corresponding value of z.

42

Step-by-step explanation:

I took the test and got it correct.