Solve {l}{2x-5y=1}{x-3y=1x-2}

$$\left\{ \begin{array} { l } { 2 x - 5 y = 1 } \\ { x - 3 y = 1 x - 2 } \end{array} \right.$$

Solve for x, y

$$x = \frac{13}{6} = 2\frac{1}{6} \approx 2.166666667$$

$$y=\frac{2}{3}\approx 0.666666667$$

Solution Steps

Consider the second equation. Subtract 1x from both sides.

$$x-3y-x=-2$$

Combine x and -x to get 0.

$$-3y=-2$$

Divide both sides by -3.

$$y=\frac{-2}{-3}$$

Fraction \frac{-2}{-3} can be simplified to \frac{2}{3} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{2}{3}$$

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

$$2x-5\times \frac{2}{3}=1$$

Multiply -5 and \frac{2}{3} to get -\frac{10}{3}.

$$2x-\frac{10}{3}=1$$

Add \frac{10}{3} to both sides.

$$2x=1+\frac{10}{3}$$

Add 1 and \frac{10}{3} to get \frac{13}{3}.

$$2x=\frac{13}{3}$$

Divide both sides by 2.

$$x=\frac{\frac{13}{3}}{2}$$

Express \frac{\frac{13}{3}}{2} as a single fraction.

$$x=\frac{13}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x=\frac{13}{6}$$

The system is now solved.

$$x=\frac{13}{6} y=\frac{2}{3}$$