Solve {l}{2{(0*251*4*472.578+0.7486y)}=321.487}{y=0.1449x+0.2739*472.578+0.5812y}{z=x-0}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 2 {(0 \cdot 251 \cdot 4 \cdot 472.578 + 0.7486 y)} = 321.487 }\\ { y = 0.1449 x + 0.2739 \cdot 472.578 + 0.5812 y }\\ { z = x - 0 }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, x, z, a

$$a = -\frac{35212789393}{129133500} = -272\frac{88477393}{129133500} \approx -272.6851622$$

Solution Steps

Consider the first equation. Divide both sides by 2.

$$0\times 251\times 4\times 472.578+0.7486y=\frac{321.487}{2}$$

Expand \frac{321.487}{2} by multiplying both numerator and the denominator by 1000.

$$0\times 251\times 4\times 472.578+0.7486y=\frac{321487}{2000}$$

Multiply 0 and 251 to get 0.

$$0\times 4\times 472.578+0.7486y=\frac{321487}{2000}$$

Multiply 0 and 4 to get 0.

$$0\times 472.578+0.7486y=\frac{321487}{2000}$$

Multiply 0 and 472.578 to get 0.

$$0+0.7486y=\frac{321487}{2000}$$

Anything plus zero gives itself.

$$0.7486y=\frac{321487}{2000}$$

Divide both sides by 0.7486.

$$y=\frac{\frac{321487}{2000}}{0.7486}$$

Express \frac{\frac{321487}{2000}}{0.7486} as a single fraction.

$$y=\frac{321487}{2000\times 0.7486}$$

Multiply 2000 and 0.7486 to get 1497.2.

$$y=\frac{321487}{1497.2}$$

Expand \frac{321487}{1497.2} by multiplying both numerator and the denominator by 10.

$$y=\frac{3214870}{14972}$$

Reduce the fraction \frac{3214870}{14972} to lowest terms by extracting and canceling out 2.

$$y=\frac{1607435}{7486}$$

Consider the second equation. Insert the known values of variables into the equation.

$$\frac{1607435}{7486}=0.1449x+0.2739\times 472.578+0.5812\times \frac{1607435}{7486}$$

Multiply 0.2739 and 472.578 to get 129.4391142.

$$\frac{1607435}{7486}=0.1449x+129.4391142+0.5812\times \frac{1607435}{7486}$$

Multiply 0.5812 and \frac{1607435}{7486} to get \frac{467120611}{3743000}.

$$\frac{1607435}{7486}=0.1449x+129.4391142+\frac{467120611}{3743000}$$

Add 129.4391142 and \frac{467120611}{3743000} to get \frac{4758056077253}{18715000000}.

$$\frac{1607435}{7486}=0.1449x+\frac{4758056077253}{18715000000}$$

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

$$0.1449x+\frac{4758056077253}{18715000000}=\frac{1607435}{7486}$$

Subtract \frac{4758056077253}{18715000000} from both sides.

$$0.1449x=\frac{1607435}{7486}-\frac{4758056077253}{18715000000}$$

Subtract \frac{4758056077253}{18715000000} from \frac{1607435}{7486} to get -\frac{739468577253}{18715000000}.

$$0.1449x=-\frac{739468577253}{18715000000}$$

Divide both sides by 0.1449.

$$x=\frac{-\frac{739468577253}{18715000000}}{0.1449}$$

Express \frac{-\frac{739468577253}{18715000000}}{0.1449} as a single fraction.

$$x=\frac{-739468577253}{18715000000\times 0.1449}$$

Multiply 18715000000 and 0.1449 to get 2711803500.

$$x=\frac{-739468577253}{2711803500}$$

Reduce the fraction \frac{-739468577253}{2711803500} to lowest terms by extracting and canceling out 21.

$$x=-\frac{35212789393}{129133500}$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=-\frac{35212789393}{129133500}-0$$

Subtract 0 from -\frac{35212789393}{129133500} to get -\frac{35212789393}{129133500}.

$$z=-\frac{35212789393}{129133500}$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$a=-\frac{35212789393}{129133500}$$

The system is now solved.

$$y=\frac{1607435}{7486} x=-\frac{35212789393}{129133500} z=-\frac{35212789393}{129133500} a=-\frac{35212789393}{129133500}$$