Solve 106x+40y+[37.16-78(x+y)]=1.42

$$106 x + 40 y + [ 37.16 - 78 ( x + y ) ] = 1.42$$

Solve for x

$$x=\frac{19y}{14}-\frac{1787}{1400}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -78 by x+y.

$$106x+40y+37.16-78x-78y=1.42$$

Combine 106x and -78x to get 28x.

$$28x+40y+37.16-78y=1.42$$

Combine 40y and -78y to get -38y.

$$28x-38y+37.16=1.42$$

Add 38y to both sides.

$$28x+37.16=1.42+38y$$

Subtract 37.16 from both sides.

$$28x=1.42+38y-37.16$$

Subtract 37.16 from 1.42 to get -35.74.

$$28x=-35.74+38y$$

The equation is in standard form.

$$28x=38y-35.74$$

Divide both sides by 28.

$$\frac{28x}{28}=\frac{38y-35.74}{28}$$

Dividing by 28 undoes the multiplication by 28.

$$x=\frac{38y-35.74}{28}$$

Divide -35.74+38y by 28.

$$x=\frac{19y}{14}-\frac{1787}{1400}$$

Solve for y

$$y=\frac{14x}{19}+\frac{1787}{1900}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -78 by x+y.

$$106x+40y+37.16-78x-78y=1.42$$

Combine 106x and -78x to get 28x.

$$28x+40y+37.16-78y=1.42$$

Combine 40y and -78y to get -38y.

$$28x-38y+37.16=1.42$$

Subtract 28x from both sides.

$$-38y+37.16=1.42-28x$$

Subtract 37.16 from both sides.

$$-38y=1.42-28x-37.16$$

Subtract 37.16 from 1.42 to get -35.74.

$$-38y=-35.74-28x$$

The equation is in standard form.

$$-38y=-28x-35.74$$

Divide both sides by -38.

$$\frac{-38y}{-38}=\frac{-28x-35.74}{-38}$$

Dividing by -38 undoes the multiplication by -38.

$$y=\frac{-28x-35.74}{-38}$$

Divide -35.74-28x by -38.

$$y=\frac{14x}{19}+\frac{1787}{1900}$$