Solve {l}{A/12=x/17}{13^2=12*17-A*}

$$\left. \begin{array} { l } { \frac { A } { 12 } = \frac { x } { 17 } } \\ { 13 ^ { 2 } = 12 \times 17 - A \times } \end{array} \right.$$

Solve for A, x

$$x = \frac{595}{12} = 49\frac{7}{12} \approx 49.583333333$$

$$A=35$$

Solution Steps

Consider the second equation. Calculate 13 to the power of 2 and get 169.

$$169=12\times 17-A$$

Multiply 12 and 17 to get 204.

$$169=204-A$$

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

$$204-A=169$$

Subtract 204 from both sides.

$$-A=169-204$$

Subtract 204 from 169 to get -35.

$$-A=-35$$

Divide both sides by -1.

$$A=\frac{-35}{-1}$$

Fraction \frac{-35}{-1} can be simplified to 35 by removing the negative sign from both the numerator and the denominator.

$$A=35$$

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

$$\frac{35}{12}=\frac{x}{17}$$

Multiply both sides of the equation by 204, the least common multiple of 12,17.

$$17\times 35=12x$$

Multiply 17 and 35 to get 595.

$$595=12x$$

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

$$12x=595$$

Divide both sides by 12.

$$x=\frac{595}{12}$$

The system is now solved.

$$A=35 x=\frac{595}{12}$$