Solve {l}{-a=1/2}{b=7a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { -a = \frac{1}{2} }\\ { b = 7 a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for a, b, c

$$c = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Solution Steps

Consider the first equation. Divide both sides by -1.

$$a=\frac{\frac{1}{2}}{-1}$$

Express \frac{\frac{1}{2}}{-1} as a single fraction.

$$a=\frac{1}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$a=\frac{1}{-2}$$

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$a=-\frac{1}{2}$$

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

$$b=7\left(-\frac{1}{2}\right)$$

Multiply 7 and -\frac{1}{2} to get -\frac{7}{2}.

$$b=-\frac{7}{2}$$

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

$$c=-\frac{7}{2}$$

The system is now solved.

$$a=-\frac{1}{2} b=-\frac{7}{2} c=-\frac{7}{2}$$