Solve {r}{-5x+6y=-22}{x-3y=19x-3y+1}

$$\left. \begin{array} { r } { - 5 x + 6 y = - 22 } \\ { x - 3 y = 19 x - 3 y + 1 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{1}{18}\approx -0.055555556$$

$$y = -\frac{401}{108} = -3\frac{77}{108} \approx -3.712962963$$

Solution Steps

Consider the second equation. Subtract 19x from both sides.

$$x-3y-19x=-3y+1$$

Combine x and -19x to get -18x.

$$-18x-3y=-3y+1$$

Add 3y to both sides.

$$-18x-3y+3y=1$$

Combine -3y and 3y to get 0.

$$-18x=1$$

Divide both sides by -18.

$$x=-\frac{1}{18}$$

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

$$-5\left(-\frac{1}{18}\right)+6y=-22$$

Multiply -5 and -\frac{1}{18} to get \frac{5}{18}.

$$\frac{5}{18}+6y=-22$$

Subtract \frac{5}{18} from both sides.

$$6y=-22-\frac{5}{18}$$

Subtract \frac{5}{18} from -22 to get -\frac{401}{18}.

$$6y=-\frac{401}{18}$$

Divide both sides by 6.

$$y=\frac{-\frac{401}{18}}{6}$$

Express \frac{-\frac{401}{18}}{6} as a single fraction.

$$y=\frac{-401}{18\times 6}$$

Multiply 18 and 6 to get 108.

$$y=\frac{-401}{108}$$

Fraction \frac{-401}{108} can be rewritten as -\frac{401}{108} by extracting the negative sign.

$$y=-\frac{401}{108}$$

The system is now solved.

$$x=-\frac{1}{18} y=-\frac{401}{108}$$