Solve {l}{6{(0*4x-1*4)}=-3*9{(1*2x-0*9)}}{y=2}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 6 {(0 \cdot 4 x - 1 \cdot 4)} = -3 \cdot 9 {(1 \cdot 2 x - 0 \cdot 9)} }\\ { y = 2 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. Multiply 0 and 4 to get 0.

$$6\left(0x-1\times 4\right)=-3\times 9\left(2x-0\times 9\right)$$

Anything times zero gives zero.

$$6\left(0-1\times 4\right)=-3\times 9\left(2x-0\times 9\right)$$

Multiply 1 and 4 to get 4.

$$6\left(0-4\right)=-3\times 9\left(2x-0\times 9\right)$$

Subtract 4 from 0 to get -4.

$$6\left(-4\right)=-3\times 9\left(2x-0\times 9\right)$$

Multiply 6 and -4 to get -24.

$$-24=-3\times 9\left(2x-0\times 9\right)$$

Multiply -3 and 9 to get -27.

$$-24=-27\left(2x-0\times 9\right)$$

Multiply 0 and 9 to get 0.

$$-24=-27\left(2x-0\right)$$

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

$$-27\left(2x-0\right)=-24$$

Divide both sides by -27.

$$2x-0=\frac{-24}{-27}$$

Reduce the fraction \frac{-24}{-27} to lowest terms by extracting and canceling out -3.

$$2x-0=\frac{8}{9}$$

Reorder the terms.

$$2x=\frac{8}{9}$$

Divide both sides by 2.

$$x=\frac{\frac{8}{9}}{2}$$

Express \frac{\frac{8}{9}}{2} as a single fraction.

$$x=\frac{8}{9\times 2}$$

Multiply 9 and 2 to get 18.

$$x=\frac{8}{18}$$

Reduce the fraction \frac{8}{18} to lowest terms by extracting and canceling out 2.

$$x=\frac{4}{9}$$

The system is now solved.

$$x=\frac{4}{9} y=2 z=2$$