Solve {l}{ab+b=2a}{5b-4=-24}

$$\left\{ \begin{array} { l } { a b + b = 2 a } \\ { 5 b - 4 = - 24 } \end{array} \right.$$

Solve for a, b

$$a=-\frac{2}{3}\approx -0.666666667$$

$$b=-4$$

Solution Steps

Consider the second equation. Add 4 to both sides.

$$5b=-24+4$$

Add -24 and 4 to get -20.

$$5b=-20$$

Divide both sides by 5.

$$b=\frac{-20}{5}$$

Divide -20 by 5 to get -4.

$$b=-4$$

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

$$a\left(-4\right)-4=2a$$

Subtract 2a from both sides.

$$a\left(-4\right)-4-2a=0$$

Combine a\left(-4\right) and -2a to get -6a.

$$-6a-4=0$$

Add 4 to both sides. Anything plus zero gives itself.

$$-6a=4$$

Divide both sides by -6.

$$a=\frac{4}{-6}$$

Reduce the fraction \frac{4}{-6} to lowest terms by extracting and canceling out 2.

$$a=-\frac{2}{3}$$

The system is now solved.

$$a=-\frac{2}{3} b=-4$$