Solve a=frac{L_{2}-L_{1}}{L_{1}(t_{2}-t_{1})}text{and}L_{1}=24.1,L_{2}=15.7,t_{1}=9.1text{and}t_{2}=6.3

$$a = \frac { L _ { 2 } - L _ { 1 } } { L _ { 1 } ( t _ { 2 } - t _ { 1 } ) } \text { and } L _ { 1 } = 24.1 , L _ { 2 } = 15.7 , t _ { 1 } = 9.1 \text { and } t _ { 2 } = 6.3$$

Solve for a, L_2, L_1, t_2, t_1

$$a=\frac{30}{241}\approx 0.124481328$$

$$L_{2}=15.7$$

$$L_{1}=24.1$$

$$t_{2}=6.3$$

$$t_{1}=9.1$$

Solution Steps

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

$$a=\frac{15.7-24.1}{24.1\left(6.3-9.1\right)}$$

Subtract 24.1 from 15.7 to get -8.4.

$$a=\frac{-8.4}{24.1\left(6.3-9.1\right)}$$

Subtract 9.1 from 6.3 to get -2.8.

$$a=\frac{-8.4}{24.1\left(-2.8\right)}$$

Multiply 24.1 and -2.8 to get -67.48.

$$a=\frac{-8.4}{-67.48}$$

Expand \frac{-8.4}{-67.48} by multiplying both numerator and the denominator by 100.

$$a=\frac{-840}{-6748}$$

Reduce the fraction \frac{-840}{-6748} to lowest terms by extracting and canceling out -28.

$$a=\frac{30}{241}$$

The system is now solved.

$$a=\frac{30}{241} L_{2}=15.7 L_{1}=24.1 t_{2}=6.3 t_{1}=9.1$$