Solve {l}{4=3x}{text{Solvefor}ytext{where}}{y=x^2-6x}

$$\left. \begin{array} { l } { 4 = 3 x }\\ { \text{Solve for } y \text{ where} } \\ { y = x ^ {2} - 6 x } \end{array} \right.$$

Solve for x, y

$$y = -\frac{56}{9} = -6\frac{2}{9} \approx -6.222222222$$

Solution Steps

Consider the first equation. Divide both sides by 3.

$$\frac{4}{3}=x$$

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

$$x=\frac{4}{3}$$

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

$$y=\left(\frac{4}{3}\right)^{2}-6\times \frac{4}{3}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$y=\frac{16}{9}-6\times \frac{4}{3}$$

Multiply -6 and \frac{4}{3} to get -8.

$$y=\frac{16}{9}-8$$

Subtract 8 from \frac{16}{9} to get -\frac{56}{9}.

$$y=-\frac{56}{9}$$

The system is now solved.

$$x=\frac{4}{3} y=-\frac{56}{9}$$