Solve {l}{13.53/13.33=x/4}{x+y=13.78}

$$\left\{ \begin{array} { l } { \frac { 13.53 } { 13.33 } = \frac { x } { 4 } } \\ { x + y = 13.78 } \end{array} \right.$$

Solve for x, y

$$x = \frac{5412}{1333} = 4\frac{80}{1333} \approx 4.060015004$$

$$y = \frac{647837}{66650} = 9\frac{47987}{66650} \approx 9.719984996$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 4.

$$4\times \frac{13.53}{13.33}=x$$

Expand \frac{13.53}{13.33} by multiplying both numerator and the denominator by 100.

$$4\times \frac{1353}{1333}=x$$

Multiply 4 and \frac{1353}{1333} to get \frac{5412}{1333}.

$$\frac{5412}{1333}=x$$

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

$$x=\frac{5412}{1333}$$

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

$$\frac{5412}{1333}+y=13.78$$

Subtract \frac{5412}{1333} from both sides.

$$y=13.78-\frac{5412}{1333}$$

Subtract \frac{5412}{1333} from 13.78 to get \frac{647837}{66650}.

$$y=\frac{647837}{66650}$$

The system is now solved.

$$x=\frac{5412}{1333} y=\frac{647837}{66650}$$