Solve {l}{0x-9y=8}{8x-15y=-1}

$$\left. \begin{array} { l } { 0 x - 9 y = 8 } \\ { 8 x - 15 y = - 1 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{43}{24} = -1\frac{19}{24} \approx -1.791666667$$

$$y=-\frac{8}{9}\approx -0.888888889$$

Solution Steps

Consider the first equation. Anything times zero gives zero.

$$0-9y=8$$

Anything plus zero gives itself.

$$-9y=8$$

Divide both sides by -9.

$$y=-\frac{8}{9}$$

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

$$8x-15\left(-\frac{8}{9}\right)=-1$$

Multiply -15 and -\frac{8}{9} to get \frac{40}{3}.

$$8x+\frac{40}{3}=-1$$

Subtract \frac{40}{3} from both sides.

$$8x=-1-\frac{40}{3}$$

Subtract \frac{40}{3} from -1 to get -\frac{43}{3}.

$$8x=-\frac{43}{3}$$

Divide both sides by 8.

$$x=\frac{-\frac{43}{3}}{8}$$

Express \frac{-\frac{43}{3}}{8} as a single fraction.

$$x=\frac{-43}{3\times 8}$$

Multiply 3 and 8 to get 24.

$$x=\frac{-43}{24}$$

Fraction \frac{-43}{24} can be rewritten as -\frac{43}{24} by extracting the negative sign.

$$x=-\frac{43}{24}$$

The system is now solved.

$$x=-\frac{43}{24} y=-\frac{8}{9}$$