Solve {l}{2.860*x+3.100*23=119.920}{y=2.860*x+3.100*23}{z=y}{a=z}{b=a}{c=b}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { 2.860 \cdot x + 3.100 \cdot 23 = 119.920 }\\ { y = 2.860 \cdot x + 3.100 \cdot 23 }\\ { z = y }\\ { a = z }\\ { b = a }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Solve for x, y, z, a, b, c, d

$$d=119.92$$

Solution Steps

Consider the first equation. Multiply 3.1 and 23 to get 71.3.

$$2.86x+71.3=119.92$$

Subtract 71.3 from both sides.

$$2.86x=119.92-71.3$$

Subtract 71.3 from 119.92 to get 48.62.

$$2.86x=48.62$$

Divide both sides by 2.86.

$$x=\frac{48.62}{2.86}$$

Expand \frac{48.62}{2.86} by multiplying both numerator and the denominator by 100.

$$x=\frac{4862}{286}$$

Divide 4862 by 286 to get 17.

$$x=17$$

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

$$y=2.86\times 17+3.1\times 23$$

Multiply 2.86 and 17 to get 48.62.

$$y=48.62+3.1\times 23$$

Multiply 3.1 and 23 to get 71.3.

$$y=48.62+71.3$$

Add 48.62 and 71.3 to get 119.92.

$$y=119.92$$

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

$$z=119.92$$

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

$$a=119.92$$

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

$$b=119.92$$

Consider the equation (6). Insert the known values of variables into the equation.

$$c=119.92$$

Consider the equation (7). Insert the known values of variables into the equation.

$$d=119.92$$

The system is now solved.

$$x=17 y=119.92 z=119.92 a=119.92 b=119.92 c=119.92 d=119.92$$