Solve x + 2y + 2z = 4; 3x - y + 4z = 25; 3x + 2y - z = - 4 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x+2y+2z=4; 3x-y+4z=25; 3x+2y-z=-4$$

Solve for x, y, z

$x=2$
$y=-3$
$z=4$

Short Steps Using Substitution

Solve $x+2y+2z=4$ for $x$.

$$x=4-2y-2z$$

Substitute $4-2y-2z$ for $x$ in the second and third equation.

$$3\left(4-2y-2z\right)-y+4z=25$$ $$3\left(4-2y-2z\right)+2y-z=-4$$

Solve these equations for $y$ and $z$ respectively.

$$y=-\frac{13}{7}-\frac{2}{7}z$$ $$z=\frac{16}{7}-\frac{4}{7}y$$

Substitute $-\frac{13}{7}-\frac{2}{7}z$ for $y$ in the equation $z=\frac{16}{7}-\frac{4}{7}y$.

$$z=\frac{16}{7}-\frac{4}{7}\left(-\frac{13}{7}-\frac{2}{7}z\right)$$

Solve $z=\frac{16}{7}-\frac{4}{7}\left(-\frac{13}{7}-\frac{2}{7}z\right)$ for $z$.

$$z=4$$

Substitute $4$ for $z$ in the equation $y=-\frac{13}{7}-\frac{2}{7}z$.

$$y=-\frac{13}{7}-\frac{2}{7}\times 4$$

Calculate $y$ from $y=-\frac{13}{7}-\frac{2}{7}\times 4$.

$$y=-3$$

Substitute $-3$ for $y$ and $4$ for $z$ in the equation $x=4-2y-2z$.

$$x=4-2\left(-3\right)-2\times 4$$

Calculate $x$ from $x=4-2\left(-3\right)-2\times 4$.

$$x=2$$

The system is now solved.

$$x=2$$ $$y=-3$$ $$z=4$$