Solve {c}{x=-4}{3x-5y=9}{6x-6y=c}

$$\left. \begin{array} { c } { x = - 4 } \\ { 3 x - 5 y = 9 } \\ { 6 x - 6 y = c } \end{array} \right.$$

Solve for x, y, c

$$x=-4$$

$$y = -\frac{21}{5} = -4\frac{1}{5} = -4.2$$

$$c = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Solution Steps

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

$$3\left(-4\right)-5y=9$$

Multiply 3 and -4 to get -12.

$$-12-5y=9$$

Add 12 to both sides.

$$-5y=9+12$$

Add 9 and 12 to get 21.

$$-5y=21$$

Divide both sides by -5.

$$y=-\frac{21}{5}$$

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

$$6\left(-4\right)-6\left(-\frac{21}{5}\right)=c$$

Multiply 6 and -4 to get -24.

$$-24-6\left(-\frac{21}{5}\right)=c$$

Multiply -6 and -\frac{21}{5} to get \frac{126}{5}.

$$-24+\frac{126}{5}=c$$

Add -24 and \frac{126}{5} to get \frac{6}{5}.

$$\frac{6}{5}=c$$

Swap sides so that all variable terms are on the left hand side.

$$c=\frac{6}{5}$$

The system is now solved.

$$x=-4 y=-\frac{21}{5} c=\frac{6}{5}$$