Answer:
(x, y, z) = (-2, 5, 3)
Explanation:
You want an algebraic solution to the system of equations ...
- 2x + 3y - 4x = -1
- x - 2y + 5z = 3
- -4x + y + z = 16
Substitution
The second equation suggests an expression for x:
x = 2y -5z +3
Substituting this into the first and third equations, we have ...
2(2y -5z +3) +3y -4z = -1 ⇒ 7y -14z = -7 ⇒ y -2z = -1
-4(2y -5z +3) +y +z = 16 ⇒ -7y +21z = 28 ⇒ y -3z = -4
These equations are reduced to standard form by dividing by the leading coefficient.
Elimination
Subtracting the second of these equations from the first, we have ...
(y -2z) -(y -3z) = (-1) -(-4)
z = 3 . . . . . . . simplify
The first of these reduced equations tells us ...
y = 2z -1 = 2(3) -1 = 5
And our original substitution equation says ...
x = 2y -5z +3 = 2(5) -5(3) +3 = -2
The solution is (x, y, z) = (-2, 5, 3).
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Additional comment
A calculator confirms this solution. The "work" is entering the correct coefficients into the appropriate calculator function, then interpreting the result.