Solve {l}{5/4x+883/256=-1/4{(-3/8x-frac{1}{2})}}{y=7151*7*12{(8*19)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{5}{4} x + \frac{883}{256} = -\frac{1}{4} {(-\frac{3}{8} x - \frac{1}{2})} }\\ { y = 7151 \cdot 7 \cdot 12 {(8 \cdot 19)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=91303968$$

Solution Steps

Consider the first equation. Use the distributive property to multiply -\frac{1}{4} by -\frac{3}{8}x-\frac{1}{2}.

$$\frac{5}{4}x+\frac{883}{256}=\frac{3}{32}x+\frac{1}{8}$$

Subtract \frac{3}{32}x from both sides.

$$\frac{5}{4}x+\frac{883}{256}-\frac{3}{32}x=\frac{1}{8}$$

Combine \frac{5}{4}x and -\frac{3}{32}x to get \frac{37}{32}x.

$$\frac{37}{32}x+\frac{883}{256}=\frac{1}{8}$$

Subtract \frac{883}{256} from both sides.

$$\frac{37}{32}x=\frac{1}{8}-\frac{883}{256}$$

Subtract \frac{883}{256} from \frac{1}{8} to get -\frac{851}{256}.

$$\frac{37}{32}x=-\frac{851}{256}$$

Multiply both sides by \frac{32}{37}, the reciprocal of \frac{37}{32}.

$$x=-\frac{851}{256}\times \frac{32}{37}$$

Multiply -\frac{851}{256} and \frac{32}{37} to get -\frac{23}{8}.

$$x=-\frac{23}{8}$$

Consider the second equation. Multiply 7151 and 7 to get 50057.

$$y=50057\times 12\times 8\times 19$$

Multiply 50057 and 12 to get 600684.

$$y=600684\times 8\times 19$$

Multiply 600684 and 8 to get 4805472.

$$y=4805472\times 19$$

Multiply 4805472 and 19 to get 91303968.

$$y=91303968$$

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

$$z=91303968$$

The system is now solved.

$$x=-\frac{23}{8} y=91303968 z=91303968$$