Question

Obtain the solution set of the system x – 3y + 4z = 9, 4x + 3y + 2z = 7, y – 2x = 5 – 10z by
elimination.

Answer 1

Answer on question #44539 – Math - Linear Algebra

Obtain the solution set of the system $x - 3y + 4z = 9$, $4x + 3y + 2z = 7$, $y - 2x = 5 - 10z$ by elimination.

Solution :

$$x - 3y + 4z = 9$$ $$4x + 3y + 2z = 7$$ $$-2x + y + 10z = 5$$

(1)+(3):

$$5x + 6z = 16$$

(1)+3*(3):

$$-5x + 34z = 24$$

(5)+(4):

$$40z = 40 \iff z = 1$$

(4)-6*(6):

$$5x = 10 \iff x = 2$$

(1)-(7) - 4*(6):

$$-3y = 9 - 2 - 4 \iff y = -1.$$

Answer: $x = 2$, $y = -1$, $z = 1$.

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