Solve {l}{9x^2-14x=y}{9x-14=1}

$$\left\{ \begin{array} { l } { 9 x ^ { 2 } - 14 x = y } \\ { 9 x - 14 = 1 } \end{array} \right.$$

Solve for x, y

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$y = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Solution Steps

Consider the second equation. Add 14 to both sides.

$$9x=1+14$$

Add 1 and 14 to get 15.

$$9x=15$$

Divide both sides by 9.

$$x=\frac{15}{9}$$

Reduce the fraction \frac{15}{9} to lowest terms by extracting and canceling out 3.

$$x=\frac{5}{3}$$

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

$$9\times \left(\frac{5}{3}\right)^{2}-14\times \frac{5}{3}=y$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$9\times \frac{25}{9}-14\times \frac{5}{3}=y$$

Multiply 9 and \frac{25}{9} to get 25.

$$25-14\times \frac{5}{3}=y$$

Multiply -14 and \frac{5}{3} to get -\frac{70}{3}.

$$25-\frac{70}{3}=y$$

Subtract \frac{70}{3} from 25 to get \frac{5}{3}.

$$\frac{5}{3}=y$$

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

$$y=\frac{5}{3}$$

The system is now solved.

$$x=\frac{5}{3} y=\frac{5}{3}$$