Solve {l}{4x+7=11.75}{5x+12y=12.25}

$$\left. \begin{array} { l } { 4 x + 7 = 11.75 } \\ { 5 x + 12 y = 12.25 } \end{array} \right.$$

Solve for x, y

$$x=1.1875$$

$$y=\frac{101}{192}\approx 0.526041667$$

Solution Steps

Consider the first equation. Subtract 7 from both sides.

$$4x=11.75-7$$

Subtract 7 from 11.75 to get 4.75.

$$4x=4.75$$

Divide both sides by 4.

$$x=\frac{4.75}{4}$$

Expand \frac{4.75}{4} by multiplying both numerator and the denominator by 100.

$$x=\frac{475}{400}$$

Reduce the fraction \frac{475}{400} to lowest terms by extracting and canceling out 25.

$$x=\frac{19}{16}$$

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

$$5\times \frac{19}{16}+12y=12.25$$

Multiply 5 and \frac{19}{16} to get \frac{95}{16}.

$$\frac{95}{16}+12y=12.25$$

Subtract \frac{95}{16} from both sides.

$$12y=12.25-\frac{95}{16}$$

Subtract \frac{95}{16} from 12.25 to get \frac{101}{16}.

$$12y=\frac{101}{16}$$

Divide both sides by 12.

$$y=\frac{\frac{101}{16}}{12}$$

Express \frac{\frac{101}{16}}{12} as a single fraction.

$$y=\frac{101}{16\times 12}$$

Multiply 16 and 12 to get 192.

$$y=\frac{101}{192}$$

The system is now solved.

$$x=\frac{19}{16} y=\frac{101}{192}$$