Solve 0.69x+0.52y=0.61(x+y)

$$0.69x+0.52y = 0.61(x+y)$$

Solve for x

$$x=\frac{9y}{8}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.61 by x+y.

$$0.69x+0.52y=0.61x+0.61y$$

Subtract 0.61x from both sides.

$$0.69x+0.52y-0.61x=0.61y$$

Combine 0.69x and -0.61x to get 0.08x.

$$0.08x+0.52y=0.61y$$

Subtract 0.52y from both sides.

$$0.08x=0.61y-0.52y$$

Combine 0.61y and -0.52y to get 0.09y.

$$0.08x=0.09y$$

The equation is in standard form.

$$0.08x=\frac{9y}{100}$$

Divide both sides of the equation by 0.08, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.08x}{0.08}=\frac{9y}{0.08\times 100}$$

Dividing by 0.08 undoes the multiplication by 0.08.

$$x=\frac{9y}{0.08\times 100}$$

Divide \frac{9y}{100} by 0.08 by multiplying \frac{9y}{100} by the reciprocal of 0.08.

$$x=\frac{9y}{8}$$

Solve for y

$$y=\frac{8x}{9}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.61 by x+y.

$$0.69x+0.52y=0.61x+0.61y$$

Subtract 0.61y from both sides.

$$0.69x+0.52y-0.61y=0.61x$$

Combine 0.52y and -0.61y to get -0.09y.

$$0.69x-0.09y=0.61x$$

Subtract 0.69x from both sides.

$$-0.09y=0.61x-0.69x$$

Combine 0.61x and -0.69x to get -0.08x.

$$-0.09y=-0.08x$$

The equation is in standard form.

$$-0.09y=-\frac{2x}{25}$$

Divide both sides of the equation by -0.09, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-0.09y}{-0.09}=-\frac{\frac{2x}{25}}{-0.09}$$

Dividing by -0.09 undoes the multiplication by -0.09.

$$y=-\frac{\frac{2x}{25}}{-0.09}$$

Divide -\frac{2x}{25} by -0.09 by multiplying -\frac{2x}{25} by the reciprocal of -0.09.

$$y=\frac{8x}{9}$$