Solve x + y + z = 4; 3x + 7 = 11; y - z = 7 | 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

$$x+y+z=4; 3x+7=11; y-z=7$$

Solve for x, y, z

$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$
$y = \frac{29}{6} = 4\frac{5}{6} \approx 4.833333333$
$z = -\frac{13}{6} = -2\frac{1}{6} \approx -2.166666667$

Short Steps Using Substitution

Solve $x+y+z=4$ for $x$.

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

Substitute $-y-z+4$ for $x$ in the equation $3x+7=11$.

$$3\left(-y-z+4\right)+7=11$$

Solve the second equation for $y$ and the third equation for $z$.

$$y=\frac{8}{3}-z$$ $$z=y-7$$

Substitute $\frac{8}{3}-z$ for $y$ in the equation $z=y-7$.

$$z=\frac{8}{3}-z-7$$

Solve $z=\frac{8}{3}-z-7$ for $z$.

$$z=-\frac{13}{6}$$

Substitute $-\frac{13}{6}$ for $z$ in the equation $y=\frac{8}{3}-z$.

$$y=\frac{8}{3}-\left(-\frac{13}{6}\right)$$

Calculate $y$ from $y=\frac{8}{3}-\left(-\frac{13}{6}\right)$.

$$y=\frac{29}{6}$$

Substitute $\frac{29}{6}$ for $y$ and $-\frac{13}{6}$ for $z$ in the equation $x=-y-z+4$.

$$x=-\frac{29}{6}-\left(-\frac{13}{6}\right)+4$$

Calculate $x$ from $x=-\frac{29}{6}-\left(-\frac{13}{6}\right)+4$.

$$x=\frac{4}{3}$$

The system is now solved.

$$x=\frac{4}{3}$$ $$y=\frac{29}{6}$$ $$z=-\frac{13}{6}$$