Solve {l}{124+20x=112}{42x+20y=144}

$$\left\{ \begin{array} { l } { 124 + 20 x = 112 } \\ { 42 x + 20 y = 144 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{3}{5}=-0.6$$

$$y = \frac{423}{50} = 8\frac{23}{50} = 8.46$$

Solution Steps

Consider the first equation. Subtract 124 from both sides.

$$20x=112-124$$

Subtract 124 from 112 to get -12.

$$20x=-12$$

Divide both sides by 20.

$$x=\frac{-12}{20}$$

Reduce the fraction \frac{-12}{20} to lowest terms by extracting and canceling out 4.

$$x=-\frac{3}{5}$$

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

$$42\left(-\frac{3}{5}\right)+20y=144$$

Multiply 42 and -\frac{3}{5} to get -\frac{126}{5}.

$$-\frac{126}{5}+20y=144$$

Add \frac{126}{5} to both sides.

$$20y=144+\frac{126}{5}$$

Add 144 and \frac{126}{5} to get \frac{846}{5}.

$$20y=\frac{846}{5}$$

Divide both sides by 20.

$$y=\frac{\frac{846}{5}}{20}$$

Express \frac{\frac{846}{5}}{20} as a single fraction.

$$y=\frac{846}{5\times 20}$$

Multiply 5 and 20 to get 100.

$$y=\frac{846}{100}$$

Reduce the fraction \frac{846}{100} to lowest terms by extracting and canceling out 2.

$$y=\frac{423}{50}$$

The system is now solved.

$$x=-\frac{3}{5} y=\frac{423}{50}$$