Solve x + 4y + 3z = 10; 2x + y - z = - 1; 3x - y + z = 11 | 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

$$x+4y+3z=10; 2x+y-z=-1; 3x-y+z=11$$

Solve for x, y, z

$x=2$
$y=-1$
$z=4$

Short Steps Using Substitution

Solve $x+4y+3z=10$ for $x$.

$$x=-4y-3z+10$$

Substitute $-4y-3z+10$ for $x$ in the second and third equation.

$$2\left(-4y-3z+10\right)+y-z=-1$$ $$3\left(-4y-3z+10\right)-y+z=11$$

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

$$y=3-z$$ $$z=-\frac{13}{8}y+\frac{19}{8}$$

Substitute $3-z$ for $y$ in the equation $z=-\frac{13}{8}y+\frac{19}{8}$.

$$z=-\frac{13}{8}\left(3-z\right)+\frac{19}{8}$$

Solve $z=-\frac{13}{8}\left(3-z\right)+\frac{19}{8}$ for $z$.

$$z=4$$

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

$$y=3-4$$

Calculate $y$ from $y=3-4$.

$$y=-1$$

Substitute $-1$ for $y$ and $4$ for $z$ in the equation $x=-4y-3z+10$.

$$x=-4\left(-1\right)-3\times 4+10$$

Calculate $x$ from $x=-4\left(-1\right)-3\times 4+10$.

$$x=2$$

The system is now solved.

$$x=2$$ $$y=-1$$ $$z=4$$