Solve 53/a+42b=12

$$\frac { 53 } { a } + 42 b = 12$$

Solve for a

$$a=-\frac{53}{6\left(7b-2\right)}$$

$$b\neq \frac{2}{7}$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$53+42ba=12a$$

Subtract 12a from both sides.

$$53+42ba-12a=0$$

Subtract 53 from both sides. Anything subtracted from zero gives its negation.

$$42ba-12a=-53$$

Combine all terms containing a.

$$\left(42b-12\right)a=-53$$

Divide both sides by 42b-12.

$$\frac{\left(42b-12\right)a}{42b-12}=-\frac{53}{42b-12}$$

Dividing by 42b-12 undoes the multiplication by 42b-12.

$$a=-\frac{53}{42b-12}$$

Divide -53 by 42b-12.

$$a=-\frac{53}{6\left(7b-2\right)}$$

Variable a cannot be equal to 0.

$$a=-\frac{53}{6\left(7b-2\right)}\text{, }a\neq 0$$

Solve for b

$$b=\frac{2}{7}-\frac{53}{42a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$53+42ba=12a$$

Subtract 53 from both sides.

$$42ba=12a-53$$

The equation is in standard form.

$$42ab=12a-53$$

Divide both sides by 42a.

$$\frac{42ab}{42a}=\frac{12a-53}{42a}$$

Dividing by 42a undoes the multiplication by 42a.

$$b=\frac{12a-53}{42a}$$

Divide 12a-53 by 42a.

$$b=\frac{2}{7}-\frac{53}{42a}$$