Solve {l}{5y+6y-81=7y+102+65y}{16+7x-5+x=11x-3-x}

$$\left. \begin{array} { l } { 5 y + 6 y - 81 = 7 y + 102 + 65 y } \\ { 16 + 7 x - 5 + x = 11 x - 3 - x } \end{array} \right.$$

Solve for y, x

$$x=7$$

$$y=-3$$

Solution Steps

Consider the first equation. Combine 5y and 6y to get 11y.

$$11y-81=7y+102+65y$$

Combine 7y and 65y to get 72y.

$$11y-81=72y+102$$

Subtract 72y from both sides.

$$11y-81-72y=102$$

Combine 11y and -72y to get -61y.

$$-61y-81=102$$

Add 81 to both sides.

$$-61y=102+81$$

Add 102 and 81 to get 183.

$$-61y=183$$

Divide both sides by -61.

$$y=\frac{183}{-61}$$

Divide 183 by -61 to get -3.

$$y=-3$$

Consider the second equation. Subtract 5 from 16 to get 11.

$$11+7x+x=11x-3-x$$

Combine 7x and x to get 8x.

$$11+8x=11x-3-x$$

Combine 11x and -x to get 10x.

$$11+8x=10x-3$$

Subtract 10x from both sides.

$$11+8x-10x=-3$$

Combine 8x and -10x to get -2x.

$$11-2x=-3$$

Subtract 11 from both sides.

$$-2x=-3-11$$

Subtract 11 from -3 to get -14.

$$-2x=-14$$

Divide both sides by -2.

$$x=\frac{-14}{-2}$$

Divide -14 by -2 to get 7.

$$x=7$$

The system is now solved.

$$y=-3 x=7$$