Solve {l}{3x-1y-12=0}{-6x+30=0}

$$\left\{ \begin{array} { l } { 3 x - 1 y - 12 = 0 } \\ { - 6 x + 30 = 0 } \end{array} \right.$$

Solve for x, y

$$x=5$$

$$y=3$$

Solution Steps

Consider the second equation. Subtract 30 from both sides. Anything subtracted from zero gives its negation.

$$-6x=-30$$

Divide both sides by -6.

$$x=\frac{-30}{-6}$$

Divide -30 by -6 to get 5.

$$x=5$$

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

$$3\times 5-y-12=0$$

Multiply 3 and 5 to get 15.

$$15-y-12=0$$

Subtract 12 from 15 to get 3.

$$3-y=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-y=-3$$

Divide both sides by -1.

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

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$y=3$$

The system is now solved.

$$x=5 y=3$$