Solve 4x + 2y - z = 1; 5x + 3y - 2z = 2; 3x + 2y - 3z = 0 | 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

$$\begin{cases}4x+2y-z=1\\ 5x+3y-2z=2\\ 3x+2y-3z=0\end{cases}$$

Solve for x, y, z

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

Short Steps Using Substitution

Solve $4x+2y-z=1$ for $z$.

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

Substitute $4x+2y-1$ for $z$ in the second and third equation.

$$5x+3y-2\left(4x+2y-1\right)=2$$ $$3x+2y-3\left(4x+2y-1\right)=0$$

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

$$y=-3x$$ $$x=-\frac{4}{9}y+\frac{1}{3}$$

Substitute $-3x$ for $y$ in the equation $x=-\frac{4}{9}y+\frac{1}{3}$.

$$x=-\frac{4}{9}\left(-3\right)x+\frac{1}{3}$$

Solve $x=-\frac{4}{9}\left(-3\right)x+\frac{1}{3}$ for $x$.

$$x=-1$$

Substitute $-1$ for $x$ in the equation $y=-3x$.

$$y=-3\left(-1\right)$$

Calculate $y$ from $y=-3\left(-1\right)$.

$$y=3$$

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

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

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

$$z=1$$

The system is now solved.

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