Solve 4x - y + 2z = 6; 3x + 2y - z = 18; 2x - y + 3z = - 1 | 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

$$4x-y+2z=6; 3x+2y-z=18; 2x-y+3z=-1$$

Solve for x, y, z

$x=3$
$y=4$
$z=-1$

Short Steps Using Substitution

Solve $4x-y+2z=6$ for $y$.

$$y=-6+4x+2z$$

Substitute $-6+4x+2z$ for $y$ in the second and third equation.

$$3x+2\left(-6+4x+2z\right)-z=18$$ $$2x-\left(-6+4x+2z\right)+3z=-1$$

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

$$x=\frac{30}{11}-\frac{3}{11}z$$ $$z=2x-7$$

Substitute $\frac{30}{11}-\frac{3}{11}z$ for $x$ in the equation $z=2x-7$.

$$z=2\left(\frac{30}{11}-\frac{3}{11}z\right)-7$$

Solve $z=2\left(\frac{30}{11}-\frac{3}{11}z\right)-7$ for $z$.

$$z=-1$$

Substitute $-1$ for $z$ in the equation $x=\frac{30}{11}-\frac{3}{11}z$.

$$x=\frac{30}{11}-\frac{3}{11}\left(-1\right)$$

Calculate $x$ from $x=\frac{30}{11}-\frac{3}{11}\left(-1\right)$.

$$x=3$$

Substitute $3$ for $x$ and $-1$ for $z$ in the equation $y=-6+4x+2z$.

$$y=-6+4\times 3+2\left(-1\right)$$

Calculate $y$ from $y=-6+4\times 3+2\left(-1\right)$.

$$y=4$$

The system is now solved.

$$x=3$$ $$y=4$$ $$z=-1$$