Solve {l}{7(x)=-3x+2}{g(x)=2x^2-3x}

$$\left. \begin{array} { l } { 7 ( x ) = - 3 x + 2 } \\ { g ( x ) = 2 x ^ { 2 } - 3 x } \end{array} \right.$$

Solve for x, g

$$x=\frac{1}{5}=0.2$$

$$g = -\frac{13}{5} = -2\frac{3}{5} = -2.6$$

Solution Steps

Consider the first equation. Add 3x to both sides.

$$7x+3x=2$$

Combine 7x and 3x to get 10x.

$$10x=2$$

Divide both sides by 10.

$$x=\frac{2}{10}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{1}{5}$$

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

$$g\times \frac{1}{5}=2\times \left(\frac{1}{5}\right)^{2}-3\times \frac{1}{5}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$g\times \frac{1}{5}=2\times \frac{1}{25}-3\times \frac{1}{5}$$

Multiply 2 and \frac{1}{25} to get \frac{2}{25}.

$$g\times \frac{1}{5}=\frac{2}{25}-3\times \frac{1}{5}$$

Multiply -3 and \frac{1}{5} to get -\frac{3}{5}.

$$g\times \frac{1}{5}=\frac{2}{25}-\frac{3}{5}$$

Subtract \frac{3}{5} from \frac{2}{25} to get -\frac{13}{25}.

$$g\times \frac{1}{5}=-\frac{13}{25}$$

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$g=-\frac{13}{25}\times 5$$

Multiply -\frac{13}{25} and 5 to get -\frac{13}{5}.

$$g=-\frac{13}{5}$$

The system is now solved.

$$x=\frac{1}{5} g=-\frac{13}{5}$$