Solve {l}{3x+101-4x-33=108-16x-100}{14-12x+39x-18x=256-6nx-657}

$$\left. \begin{array} { l } { 3 x + 101 - 4 x - 33 = 108 - 16 x - 100 } \\ { 14 - 12 x + 39 x - 18 x = 256 - 6 n x - 657 } \end{array} \right.$$

Solve for x, n

$$x=-4$$

$$n = \frac{379}{24} = 15\frac{19}{24} \approx 15.791666667$$

Solution Steps

Consider the first equation. Combine 3x and -4x to get -x.

$$-x+101-33=108-16x-100$$

Subtract 33 from 101 to get 68.

$$-x+68=108-16x-100$$

Subtract 100 from 108 to get 8.

$$-x+68=8-16x$$

Add 16x to both sides.

$$-x+68+16x=8$$

Combine -x and 16x to get 15x.

$$15x+68=8$$

Subtract 68 from both sides.

$$15x=8-68$$

Subtract 68 from 8 to get -60.

$$15x=-60$$

Divide both sides by 15.

$$x=\frac{-60}{15}$$

Divide -60 by 15 to get -4.

$$x=-4$$

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

$$14-12\left(-4\right)+39\left(-4\right)-18\left(-4\right)=256-6n\left(-4\right)-657$$

Do the multiplications.

$$14+48-156+72=256-6n\left(-4\right)-657$$

Add 14 and 48 to get 62.

$$62-156+72=256-6n\left(-4\right)-657$$

Subtract 156 from 62 to get -94.

$$-94+72=256-6n\left(-4\right)-657$$

Add -94 and 72 to get -22.

$$-22=256-6n\left(-4\right)-657$$

Multiply -6 and -4 to get 24.

$$-22=256+24n-657$$

Subtract 657 from 256 to get -401.

$$-22=-401+24n$$

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

$$-401+24n=-22$$

Add 401 to both sides.

$$24n=-22+401$$

Add -22 and 401 to get 379.

$$24n=379$$

Divide both sides by 24.

$$n=\frac{379}{24}$$

The system is now solved.

$$x=-4 n=\frac{379}{24}$$