Solve {l}{x-3/2-4+1/6=22}{-9x+2y=1}

$$\left. \begin{array} { l } { \frac { x - 3 } { 2 } - \frac { 4 + 1 } { 6 } = 22 } \\ { - 9 x + 2 y = 1 } \end{array} \right.$$

Solve for x, y

$$x = \frac{146}{3} = 48\frac{2}{3} \approx 48.666666667$$

$$y = \frac{439}{2} = 219\frac{1}{2} = 219.5$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 2,6.

$$3\left(x-3\right)-\left(4+1\right)=132$$

Use the distributive property to multiply 3 by x-3.

$$3x-9-\left(4+1\right)=132$$

Add 4 and 1 to get 5.

$$3x-9-5=132$$

Subtract 5 from -9 to get -14.

$$3x-14=132$$

Add 14 to both sides.

$$3x=132+14$$

Add 132 and 14 to get 146.

$$3x=146$$

Divide both sides by 3.

$$x=\frac{146}{3}$$

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

$$-9\times \frac{146}{3}+2y=1$$

Multiply -9 and \frac{146}{3} to get -438.

$$-438+2y=1$$

Add 438 to both sides.

$$2y=1+438$$

Add 1 and 438 to get 439.

$$2y=439$$

Divide both sides by 2.

$$y=\frac{439}{2}$$

The system is now solved.

$$x=\frac{146}{3} y=\frac{439}{2}$$