Answer:
(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.
