Solve {l}{0x-7y=-5}{2x-5y=-15}

$$\left. \begin{array} { l } { 0 x - 7 y = - 5 } \\ { 2 x - 5 y = - 15 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{40}{7} = -5\frac{5}{7} \approx -5.714285714$$

$$y=\frac{5}{7}\approx 0.714285714$$

Solution Steps

Consider the first equation. Anything times zero gives zero.

$$0-7y=-5$$

Anything plus zero gives itself.

$$-7y=-5$$

Divide both sides by -7.

$$y=\frac{-5}{-7}$$

Fraction \frac{-5}{-7} can be simplified to \frac{5}{7} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{5}{7}$$

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

$$2x-5\times \frac{5}{7}=-15$$

Multiply -5 and \frac{5}{7} to get -\frac{25}{7}.

$$2x-\frac{25}{7}=-15$$

Add \frac{25}{7} to both sides.

$$2x=-15+\frac{25}{7}$$

Add -15 and \frac{25}{7} to get -\frac{80}{7}.

$$2x=-\frac{80}{7}$$

Divide both sides by 2.

$$x=\frac{-\frac{80}{7}}{2}$$

Express \frac{-\frac{80}{7}}{2} as a single fraction.

$$x=\frac{-80}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$x=\frac{-80}{14}$$

Reduce the fraction \frac{-80}{14} to lowest terms by extracting and canceling out 2.

$$x=-\frac{40}{7}$$

The system is now solved.

$$x=-\frac{40}{7} y=\frac{5}{7}$$