Solve {l}{150+60y+30=60x}{50+60y=60*1.5y*150+60y=90y}{150=30y}{5=y}

$$\left. \begin{array} { l } { 150 + 60 y + 30 = 60 x } \\ { 50 + 60 y = 60 \cdot 1.5 y \cdot 150 + 60 y = 90 y } \\ { 150 = 30 y } \\ { 5 = y } \end{array} \right.$$

Solve for y, x

$$x = \frac{811}{270} = 3\frac{1}{270} \approx 3.003703704$$

$$y=\frac{1}{270}\approx 0.003703704$$

Solution Steps

Consider the second equation. Multiply 60 and 1.5 to get 90.

$$50+60y=90y\times 150+60y$$

Multiply 90 and 150 to get 13500.

$$50+60y=13500y+60y$$

Combine 13500y and 60y to get 13560y.

$$50+60y=13560y$$

Subtract 13560y from both sides.

$$50+60y-13560y=0$$

Combine 60y and -13560y to get -13500y.

$$50-13500y=0$$

Subtract 50 from both sides. Anything subtracted from zero gives its negation.

$$-13500y=-50$$

Divide both sides by -13500.

$$y=\frac{-50}{-13500}$$

Reduce the fraction \frac{-50}{-13500} to lowest terms by extracting and canceling out -50.

$$y=\frac{1}{270}$$

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

$$150+60\times \frac{1}{270}+30=60x$$

Multiply 60 and \frac{1}{270} to get \frac{2}{9}.

$$150+\frac{2}{9}+30=60x$$

Add 150 and \frac{2}{9} to get \frac{1352}{9}.

$$\frac{1352}{9}+30=60x$$

Add \frac{1352}{9} and 30 to get \frac{1622}{9}.

$$\frac{1622}{9}=60x$$

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

$$60x=\frac{1622}{9}$$

Divide both sides by 60.

$$x=\frac{\frac{1622}{9}}{60}$$

Express \frac{\frac{1622}{9}}{60} as a single fraction.

$$x=\frac{1622}{9\times 60}$$

Multiply 9 and 60 to get 540.

$$x=\frac{1622}{540}$$

Reduce the fraction \frac{1622}{540} to lowest terms by extracting and canceling out 2.

$$x=\frac{811}{270}$$

The system is now solved.

$$y=\frac{1}{270} x=\frac{811}{270}$$