Solve x + y + z = 163; 12x + 13y + 14z = 2212; 13x + 14.5y + 15.5z = 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

$$x+y+z=163; 12x+13y+14z=2212; 13x+14.5y+15.5z=237$$

Solve for x, y, z

$x=4439$
$y=-8808$
$z=4532$

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.

$$12\left(-y-z+163\right)+13y+14z=2212$$ $$13\left(-y-z+163\right)+14.5y+15.5z=237$$

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

$$y=256-2z$$ $$z=-0.6y-752.8$$

Substitute $256-2z$ for $y$ in the equation $z=-0.6y-752.8$.

$$z=-0.6\left(256-2z\right)-752.8$$

Solve $z=-0.6\left(256-2z\right)-752.8$ for $z$.

$$z=4532$$

Substitute $4532$ for $z$ in the equation $y=256-2z$.

$$y=256-2\times 4532$$

Calculate $y$ from $y=256-2\times 4532$.

$$y=-8808$$

Substitute $-8808$ for $y$ and $4532$ for $z$ in the equation $x=-y-z+163$.

$$x=-\left(-8808\right)-4532+163$$

Calculate $x$ from $x=-\left(-8808\right)-4532+163$.

$$x=4439$$

The system is now solved.

$$x=4439$$ $$y=-8808$$ $$z=4532$$