Solve {l}{2x-y=3}{4x-7x=2}

$$\left. \begin{array} { l } { 2 x - y = 3 } \\ { 4 x - 7 x = 2 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{2}{3}\approx -0.666666667$$

$$y = -\frac{13}{3} = -4\frac{1}{3} \approx -4.333333333$$

Solution Steps

Consider the second equation. Combine 4x and -7x to get -3x.

$$-3x=2$$

Divide both sides by -3.

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

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

$$2\left(-\frac{2}{3}\right)-y=3$$

Multiply 2 and -\frac{2}{3} to get -\frac{4}{3}.

$$-\frac{4}{3}-y=3$$

Add \frac{4}{3} to both sides.

$$-y=3+\frac{4}{3}$$

Add 3 and \frac{4}{3} to get \frac{13}{3}.

$$-y=\frac{13}{3}$$

Divide both sides by -1.

$$y=\frac{\frac{13}{3}}{-1}$$

Express \frac{\frac{13}{3}}{-1} as a single fraction.

$$y=\frac{13}{3\left(-1\right)}$$

Multiply 3 and -1 to get -3.

$$y=\frac{13}{-3}$$

Fraction \frac{13}{-3} can be rewritten as -\frac{13}{3} by extracting the negative sign.

$$y=-\frac{13}{3}$$

The system is now solved.

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