Solve {l}{4=3x}{y=-1-51-{(-x)}}{z={(-25)}}{text{Solvefor}a,btext{where}}{a=y}{b=z}

$$\left. \begin{array} { l } { 4 = 3 x }\\ { y = -1 - 51 - {(-x)} }\\ { z = {(-25)} }\\ { \text{Solve for } a,b \text{ where} } \\ { a = y }\\ { b = z } \end{array} \right.$$

Solve for x, y, z, a, b

$$a = -\frac{152}{3} = -50\frac{2}{3} \approx -50.666666667$$

$$b=-25$$

Solution Steps

Consider the first equation. Divide both sides by 3.

$$\frac{4}{3}=x$$

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

$$x=\frac{4}{3}$$

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

$$y=-1-51-\left(-\frac{4}{3}\right)$$

Subtract 51 from -1 to get -52.

$$y=-52-\left(-\frac{4}{3}\right)$$

The opposite of -\frac{4}{3} is \frac{4}{3}.

$$y=-52+\frac{4}{3}$$

Add -52 and \frac{4}{3} to get -\frac{152}{3}.

$$y=-\frac{152}{3}$$

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

$$a=-\frac{152}{3}$$

The system is now solved.

$$x=\frac{4}{3} y=-\frac{152}{3} z=-25 a=-\frac{152}{3} b=-25$$