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

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

Solve for y, x

$$x=2$$

$$y = -\frac{183}{65} = -2\frac{53}{65} \approx -2.815384615$$

Solution Steps

Consider the first equation. Combine y and 6y to get 7y.

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

Combine 7y and 65y to get 72y.

$$7y-81=72y+102$$

Subtract 72y from both sides.

$$7y-81-72y=102$$

Combine 7y and -72y to get -65y.

$$-65y-81=102$$

Add 81 to both sides.

$$-65y=102+81$$

Add 102 and 81 to get 183.

$$-65y=183$$

Divide both sides by -65.

$$y=-\frac{183}{65}$$

Consider the second equation. Subtract 5 from 6 to get 1.

$$1+7x+x=11x-3-x$$

Combine 7x and x to get 8x.

$$1+8x=11x-3-x$$

Combine 11x and -x to get 10x.

$$1+8x=10x-3$$

Subtract 10x from both sides.

$$1+8x-10x=-3$$

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

$$1-2x=-3$$

Subtract 1 from both sides.

$$-2x=-3-1$$

Subtract 1 from -3 to get -4.

$$-2x=-4$$

Divide both sides by -2.

$$x=\frac{-4}{-2}$$

Divide -4 by -2 to get 2.

$$x=2$$

The system is now solved.

$$y=-\frac{183}{65} x=2$$