Solve {l}{2x+1=0}{3x-y=1}

$$\left. \begin{array} { l } { 2 x + 1 = 0 } \\ { 3 x - y = 1 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{1}{2}=-0.5$$

$$y = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Solution Steps

Consider the first equation. Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$2x=-1$$

Divide both sides by 2.

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

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

$$3\left(-\frac{1}{2}\right)-y=1$$

Multiply 3 and -\frac{1}{2} to get -\frac{3}{2}.

$$-\frac{3}{2}-y=1$$

Add \frac{3}{2} to both sides.

$$-y=1+\frac{3}{2}$$

Add 1 and \frac{3}{2} to get \frac{5}{2}.

$$-y=\frac{5}{2}$$

Divide both sides by -1.

$$y=\frac{\frac{5}{2}}{-1}$$

Express \frac{\frac{5}{2}}{-1} as a single fraction.

$$y=\frac{5}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$y=\frac{5}{-2}$$

Fraction \frac{5}{-2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$y=-\frac{5}{2}$$

The system is now solved.

$$x=-\frac{1}{2} y=-\frac{5}{2}$$