Solve {c}{-16}{-6}+x*{c}{33}{0}={c}{-4}{22}+r*{c}{0}{-33}

$$\left( \begin{array} { c } { - 16 } \\ { - 6 } \end{array} \right) + x \cdot \left( \begin{array} { c } { 33 } \\ { 0 } \end{array} \right) = \left( \begin{array} { c } { - 4 } \\ { 22 } \end{array} \right) + r \cdot \left( \begin{array} { c } { 0 } \\ { - 33 } \end{array} \right)$$

Solve for x, r

$$x=\frac{4}{11}\approx 0.363636364$$

$$r=\frac{28}{33}\approx 0.848484848$$

Solution Steps

Consider the first equation. Add 16 to both sides.

$$33x=-4+16$$

Add -4 and 16 to get 12.

$$33x=12$$

Divide both sides by 33.

$$x=\frac{12}{33}$$

Reduce the fraction \frac{12}{33} to lowest terms by extracting and canceling out 3.

$$x=\frac{4}{11}$$

Consider the second equation. Swap sides so that all variable terms are on the left hand side.

$$22-33r=-6$$

Subtract 22 from both sides.

$$-33r=-6-22$$

Subtract 22 from -6 to get -28.

$$-33r=-28$$

Divide both sides by -33.

$$r=\frac{-28}{-33}$$

Fraction \frac{-28}{-33} can be simplified to \frac{28}{33} by removing the negative sign from both the numerator and the denominator.

$$r=\frac{28}{33}$$

The system is now solved.

$$x=\frac{4}{11} r=\frac{28}{33}$$