Solve 2x + y + z = 1; x-2y 9-z=3/2; 3y - 5Z = 9 | 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

$$2x+y+z=1; x-2y\ 9-z=3/2; 3y-5Z=9$$

Solve for x, y, z

$x=1$
$y=\frac{1}{2}=0.5$
$z = -\frac{3}{2} = -1\frac{1}{2} = -1.5$

Short Steps Using Substitution

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

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

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

$$x-2\left(-2x-z+1\right)-z=\frac{3}{2}$$ $$3\left(-2x-z+1\right)-5z=9$$

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

$$x=\frac{7}{10}-\frac{1}{5}z$$ $$z=-\frac{3}{4}-\frac{3}{4}x$$

Substitute $\frac{7}{10}-\frac{1}{5}z$ for $x$ in the equation $z=-\frac{3}{4}-\frac{3}{4}x$.

$$z=-\frac{3}{4}-\frac{3}{4}\left(\frac{7}{10}-\frac{1}{5}z\right)$$

Solve $z=-\frac{3}{4}-\frac{3}{4}\left(\frac{7}{10}-\frac{1}{5}z\right)$ for $z$.

$$z=-\frac{3}{2}$$

Substitute $-\frac{3}{2}$ for $z$ in the equation $x=\frac{7}{10}-\frac{1}{5}z$.

$$x=\frac{7}{10}-\frac{1}{5}\left(-\frac{3}{2}\right)$$

Calculate $x$ from $x=\frac{7}{10}-\frac{1}{5}\left(-\frac{3}{2}\right)$.

$$x=1$$

Substitute $1$ for $x$ and $-\frac{3}{2}$ for $z$ in the equation $y=-2x-z+1$.

$$y=-2-\left(-\frac{3}{2}\right)+1$$

Calculate $y$ from $y=-2-\left(-\frac{3}{2}\right)+1$.

$$y=\frac{1}{2}$$

The system is now solved.

$$x=1$$ $$y=\frac{1}{2}$$ $$z=-\frac{3}{2}$$