Solve {l}{2x+2=6}{3x-2y=-11}

$$\left. \begin{array} { l } { 2 x + 2 = 6 } \\ { 3 x - 2 y = - 11 } \end{array} \right.$$

Solve for x, y

$$x=2$$

$$y = \frac{17}{2} = 8\frac{1}{2} = 8.5$$

Solution Steps

Consider the first equation. Subtract 2 from both sides.

$$2x=6-2$$

Subtract 2 from 6 to get 4.

$$2x=4$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x=2$$

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

$$3\times 2-2y=-11$$

Multiply 3 and 2 to get 6.

$$6-2y=-11$$

Subtract 6 from both sides.

$$-2y=-11-6$$

Subtract 6 from -11 to get -17.

$$-2y=-17$$

Divide both sides by -2.

$$y=\frac{-17}{-2}$$

Fraction \frac{-17}{-2} can be simplified to \frac{17}{2} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{17}{2}$$

The system is now solved.

$$x=2 y=\frac{17}{2}$$