Solve {l}{5250=11/2[2a+(n-1)(-15)]}{6500=n[610+(n-1)(-15)}

$$\left. \begin{array} { l } { 5250 = \frac { 11 } { 2 } [ 2 a + ( n - 1 ) ( - 15 ) ] } \\ { 6500 = n [ 610 + ( n - 1 ) ( - 15 ) } \end{array} \right.$$

Solve for a, n

$$a = \frac{1082835}{22} = 49219\frac{17}{22} \approx 49219.772727273$$

$$n=6500$$

Solution Steps

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

$$n=6500$$

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

$$5250=\frac{11}{2}\left(2a+\left(6500-1\right)\left(-15\right)\right)$$

Multiply both sides by \frac{2}{11}, the reciprocal of \frac{11}{2}.

$$5250\times \frac{2}{11}=2a+\left(6500-1\right)\left(-15\right)$$

Multiply 5250 and \frac{2}{11} to get \frac{10500}{11}.

$$\frac{10500}{11}=2a+\left(6500-1\right)\left(-15\right)$$

Subtract 1 from 6500 to get 6499.

$$\frac{10500}{11}=2a+6499\left(-15\right)$$

Multiply 6499 and -15 to get -97485.

$$\frac{10500}{11}=2a-97485$$

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

$$2a-97485=\frac{10500}{11}$$

Add 97485 to both sides.

$$2a=\frac{10500}{11}+97485$$

Add \frac{10500}{11} and 97485 to get \frac{1082835}{11}.

$$2a=\frac{1082835}{11}$$

Divide both sides by 2.

$$a=\frac{\frac{1082835}{11}}{2}$$

Express \frac{\frac{1082835}{11}}{2} as a single fraction.

$$a=\frac{1082835}{11\times 2}$$

Multiply 11 and 2 to get 22.

$$a=\frac{1082835}{22}$$

The system is now solved.

$$a=\frac{1082835}{22} n=6500$$