Solve {l}{2x+3y=18}{-5x-3x=-27}

$$\left. \begin{array} { l } { 2 x + 3 y = 18 } \\ { - 5 x - 3 x = - 27 } \end{array} \right.$$

Solve for x, y

$$x = \frac{27}{8} = 3\frac{3}{8} = 3.375$$

$$y = \frac{15}{4} = 3\frac{3}{4} = 3.75$$

Solution Steps

Consider the second equation. Combine -5x and -3x to get -8x.

$$-8x=-27$$

Divide both sides by -8.

$$x=\frac{-27}{-8}$$

Fraction \frac{-27}{-8} can be simplified to \frac{27}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{27}{8}$$

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

$$2\times \frac{27}{8}+3y=18$$

Multiply 2 and \frac{27}{8} to get \frac{27}{4}.

$$\frac{27}{4}+3y=18$$

Subtract \frac{27}{4} from both sides.

$$3y=18-\frac{27}{4}$$

Subtract \frac{27}{4} from 18 to get \frac{45}{4}.

$$3y=\frac{45}{4}$$

Divide both sides by 3.

$$y=\frac{\frac{45}{4}}{3}$$

Express \frac{\frac{45}{4}}{3} as a single fraction.

$$y=\frac{45}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$y=\frac{45}{12}$$

Reduce the fraction \frac{45}{12} to lowest terms by extracting and canceling out 3.

$$y=\frac{15}{4}$$

The system is now solved.

$$x=\frac{27}{8} y=\frac{15}{4}$$