Solve {l}{20/b=40/26}{35/a=7/2}

$$\left. \begin{array} { l } { \frac { 20 } { b } = \frac { 40 } { 26 } } \\ { \frac { 35 } { a } = \frac { 7 } { 2 } } \end{array} \right.$$

Solve for b, a

$$b=13$$

$$a=10$$

Solution Steps

Consider the first equation. Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 26b, the least common multiple of b,26.

$$26\times 20=b\times 40$$

Multiply 26 and 20 to get 520.

$$520=b\times 40$$

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

$$b\times 40=520$$

Divide both sides by 40.

$$b=\frac{520}{40}$$

Divide 520 by 40 to get 13.

$$b=13$$

Consider the second equation. Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2a, the least common multiple of a,2.

$$2\times 35=7a$$

Multiply 2 and 35 to get 70.

$$70=7a$$

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

$$7a=70$$

Divide both sides by 7.

$$a=\frac{70}{7}$$

Divide 70 by 7 to get 10.

$$a=10$$

The system is now solved.

$$b=13 a=10$$