Solve {l}{1=6x}{text{Solvefor}ytext{where}}{y=x^2-5x}

$$\left. \begin{array} { l } { 1 = 6 x }\\ { \text{Solve for } y \text{ where} } \\ { y = x ^ {2} - 5 x } \end{array} \right.$$

Solve for x, y

$$y=-\frac{29}{36}\approx -0.805555556$$

Solution Steps

Consider the first equation. Divide both sides by 6.

$$\frac{1}{6}=x$$

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

$$x=\frac{1}{6}$$

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

$$y=\left(\frac{1}{6}\right)^{2}-5\times \frac{1}{6}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$y=\frac{1}{36}-5\times \frac{1}{6}$$

Multiply -5 and \frac{1}{6} to get -\frac{5}{6}.

$$y=\frac{1}{36}-\frac{5}{6}$$

Subtract \frac{5}{6} from \frac{1}{36} to get -\frac{29}{36}.

$$y=-\frac{29}{36}$$

The system is now solved.

$$x=\frac{1}{6} y=-\frac{29}{36}$$