Type a math problem

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Type a math problem

Solve for x_1, x_2, x_3

x_{1}=9x_{4}<br/>x_{2}=-8x_{4}<br/>x_{3}=-4x_{4}

$x_{1}=9x_{4}$

$x_{2}=−8x_{4}$

$x_{3}=−4x_{4}$

$x_{2}=−8x_{4}$

$x_{3}=−4x_{4}$

Short Steps Using Substitution

\left. \begin{array} { c } { x _ { 1 } + 2 x _ { 2 } - x _ { 3 } + 3 x _ { 4 } = 0 } \\ { 2 x _ { 1 } + 3 x _ { 2 } - x _ { 3 } + 2 x _ { 4 } = 0 } \\ { x _ { 1 } \quad + 3 x _ { 3 } + 3 x _ { 4 } = 0 } \end{array} \right

Solve x_{1}+2x_{2}-x_{3}+3x_{4}=0 for x_{1}.

Solve $x_{1}+2x_{2}−x_{3}+3x_{4}=0$ for $x_{1}$.

x_{1}=-2x_{2}+x_{3}-3x_{4}

$x_{1}=−2x_{2}+x_{3}−3x_{4}$

Substitute -2x_{2}+x_{3}-3x_{4} for x_{1} in the second and third equation.

Substitute $−2x_{2}+x_{3}−3x_{4}$ for $x_{1}$ in the second and third equation.

2\left(-2x_{2}+x_{3}-3x_{4}\right)+3x_{2}-x_{3}+2x_{4}=0 -2x_{2}+x_{3}-3x_{4}+3x_{3}+3x_{4}=0

$2(−2x_{2}+x_{3}−3x_{4})+3x_{2}−x_{3}+2x_{4}=0$ $−2x_{2}+x_{3}−3x_{4}+3x_{3}+3x_{4}=0$

Solve these equations for x_{2} and x_{3} respectively.

Solve these equations for $x_{2}$ and $x_{3}$ respectively.

x_{2}=x_{3}-4x_{4} x_{3}=\frac{1}{2}x_{2}

$x_{2}=x_{3}−4x_{4}$ $x_{3}=21 x_{2}$

Substitute x_{3}-4x_{4} for x_{2} in the equation x_{3}=\frac{1}{2}x_{2}.

Substitute $x_{3}−4x_{4}$ for $x_{2}$ in the equation $x_{3}=21 x_{2}$.

x_{3}=\frac{1}{2}\left(x_{3}-4x_{4}\right)

$x_{3}=21 (x_{3}−4x_{4})$

Solve x_{3}=\frac{1}{2}\left(x_{3}-4x_{4}\right) for x_{3}.

Solve $x_{3}=21 (x_{3}−4x_{4})$ for $x_{3}$.

x_{3}=-4x_{4}

$x_{3}=−4x_{4}$

Substitute -4x_{4} for x_{3} in the equation x_{2}=x_{3}-4x_{4}.

Substitute $−4x_{4}$ for $x_{3}$ in the equation $x_{2}=x_{3}−4x_{4}$.

x_{2}=-4x_{4}-4x_{4}

$x_{2}=−4x_{4}−4x_{4}$

Calculate x_{2} from x_{2}=-4x_{4}-4x_{4}.

Calculate $x_{2}$ from $x_{2}=−4x_{4}−4x_{4}$.

x_{2}=-8x_{4}

$x_{2}=−8x_{4}$

Substitute -8x_{4} for x_{2} and -4x_{4} for x_{3} in the equation x_{1}=-2x_{2}+x_{3}-3x_{4}.

Substitute $−8x_{4}$ for $x_{2}$ and $−4x_{4}$ for $x_{3}$ in the equation $x_{1}=−2x_{2}+x_{3}−3x_{4}$.

x_{1}=-2\left(-8\right)x_{4}-4x_{4}-3x_{4}

$x_{1}=−2(−8)x_{4}−4x_{4}−3x_{4}$

Calculate x_{1} from x_{1}=-2\left(-8\right)x_{4}-4x_{4}-3x_{4}.

Calculate $x_{1}$ from $x_{1}=−2(−8)x_{4}−4x_{4}−3x_{4}$.

x_{1}=9x_{4}

$x_{1}=9x_{4}$

The system is now solved.

The system is now solved.

x_{1}=9x_{4} x_{2}=-8x_{4} x_{3}=-4x_{4}

$x_{1}=9x_{4}$ $x_{2}=−8x_{4}$ $x_{3}=−4x_{4}$

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x_{1}=-2x_{2}+x_{3}-3x_{4}

Solve x_{1}+2x_{2}-x_{3}+3x_{4}=0 for x_{1}.

2\left(-2x_{2}+x_{3}-3x_{4}\right)+3x_{2}-x_{3}+2x_{4}=0 -2x_{2}+x_{3}-3x_{4}+3x_{3}+3x_{4}=0

Substitute -2x_{2}+x_{3}-3x_{4} for x_{1} in the second and third equation.

x_{2}=x_{3}-4x_{4} x_{3}=\frac{1}{2}x_{2}

Solve these equations for x_{2} and x_{3} respectively.

x_{3}=\frac{1}{2}\left(x_{3}-4x_{4}\right)

Substitute x_{3}-4x_{4} for x_{2} in the equation x_{3}=\frac{1}{2}x_{2}.

x_{3}=-4x_{4}

Solve x_{3}=\frac{1}{2}\left(x_{3}-4x_{4}\right) for x_{3}.

x_{2}=-4x_{4}-4x_{4}

Substitute -4x_{4} for x_{3} in the equation x_{2}=x_{3}-4x_{4}.

x_{2}=-8x_{4}

Calculate x_{2} from x_{2}=-4x_{4}-4x_{4}.

x_{1}=-2\left(-8\right)x_{4}-4x_{4}-3x_{4}

Substitute -8x_{4} for x_{2} and -4x_{4} for x_{3} in the equation x_{1}=-2x_{2}+x_{3}-3x_{4}.

x_{1}=9x_{4}

Calculate x_{1} from x_{1}=-2\left(-8\right)x_{4}-4x_{4}-3x_{4}.

x_{1}=9x_{4} x_{2}=-8x_{4} x_{3}=-4x_{4}

The system is now solved.

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