Solve x + y + z = 163; 12x + 13y + 14z = 2212; x + 1.5y + 1.5z = 237 | 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

$$x+y+z=163; 12x+13y+14z=2212; x+1.5y+1.5z=237$$

Solve for x, y, z

$x=15$
$y=40$
$z=108$

Short Steps Using Substitution

Solve $x+y+z=163$ for $x$.

$$x=-y-z+163$$

Substitute $-y-z+163$ for $x$ in the second and third equation.

$$12\left(-y-z+163\right)+13y+14z=2212$$ $$-y-z+163+1.5y+1.5z=237$$

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

$$y=256-2z$$ $$z=-y+148$$

Substitute $256-2z$ for $y$ in the equation $z=-y+148$.

$$z=-\left(256-2z\right)+148$$

Solve $z=-\left(256-2z\right)+148$ for $z$.

$$z=108$$

Substitute $108$ for $z$ in the equation $y=256-2z$.

$$y=256-2\times 108$$

Calculate $y$ from $y=256-2\times 108$.

$$y=40$$

Substitute $40$ for $y$ and $108$ for $z$ in the equation $x=-y-z+163$.

$$x=-40-108+163$$

Calculate $x$ from $x=-40-108+163$.

$$x=15$$

The system is now solved.

$$x=15$$ $$y=40$$ $$z=108$$