Solve {l}{x+550=y}{.065x+0.055=567.50}

$$\left. \begin{array} { l } { x + 550 = y } \\ { .065 x + 0.055 = 567.50 } \end{array} \right.$$

Solve for x, y

$$x = \frac{113489}{13} = 8729\frac{12}{13} \approx 8729.923076923$$

$$y = \frac{120639}{13} = 9279\frac{12}{13} \approx 9279.923076923$$

Solution Steps

Consider the second equation. Subtract 0.055 from both sides.

$$0.065x=567.5-0.055$$

Subtract 0.055 from 567.5 to get 567.445.

$$0.065x=567.445$$

Divide both sides by 0.065.

$$x=\frac{567.445}{0.065}$$

Expand \frac{567.445}{0.065} by multiplying both numerator and the denominator by 1000.

$$x=\frac{567445}{65}$$

Reduce the fraction \frac{567445}{65} to lowest terms by extracting and canceling out 5.

$$x=\frac{113489}{13}$$

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

$$\frac{113489}{13}+550=y$$

Add \frac{113489}{13} and 550 to get \frac{120639}{13}.

$$\frac{120639}{13}=y$$

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

$$y=\frac{120639}{13}$$

The system is now solved.

$$x=\frac{113489}{13} y=\frac{120639}{13}$$