Solve each system of equations.2x−y+z=1x+2y−4z=34x+3y−7z=−8

Q8. - Algebra 2 | StudyQuestionHub

Solve each system of equations.

$\begin{array}{l} 2 x - y + z = 1 \\ x + 2 y - 4 z = 3 \\ 4 x + 3 y - 7 z = - 8 \end{array}$

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Answer

The solution is not possible.

1Step-1 –Using elimination to obtain two equations with two variables

Given system of equations are

$\begin{array}{l} 2 x - y + z = 1 \\ x + 2 y - 4 z = 3 \\ 4 x + 3 y - 7 z = - 8 \end{array}$

Multiplying first equation by $4$ and adding to the second equation, we get

$\begin{array}{l} 8 x + x - 4 y + 2 y = 4 + 3 \\ 9 x - 2 y = 7 \end{array}$

Again multiplying first equation by $7$ and adding to the third equation, we get

$\begin{array}{l} 14 x + 4 x - 7 y + 3 y = 7 - 8 \\ 18 x - 4 y = - 1 \end{array}$

2Step-2 –Solving the system of two equations with two variables

System of two equations with two variables are

$\begin{array}{l} 9 x - 2 y = 7 \\ 18 x - 4 y = - 1 \end{array}$

3Step-3- Solve the second equation

$\begin{array}{l} 18 x - 4 y = - 1 \\ 2 (9 x - 4 y) = - 1 \\ 2 (7) = - 1 \\ 14 = - 1 \end{array}$

Which is not possible.