Solve {l}{y=2x^2-5x+3}{x=21/4}

$$\left.\begin{array} { l } { y = 2 x ^ { 2 } - 5 x + 3 } \\ { x = 2 \frac { 1 } { 4 } } \end{array} \right\}$$

Solve for y, x

$$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

$$y = \frac{15}{8} = 1\frac{7}{8} = 1.875$$

Solution Steps

Consider the second equation. Multiply 2 and 4 to get 8.

$$x=\frac{8+1}{4}$$

Add 8 and 1 to get 9.

$$x=\frac{9}{4}$$

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

$$y=2\times \left(\frac{9}{4}\right)^{2}-5\times \frac{9}{4}+3$$

Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.

$$y=2\times \frac{81}{16}-5\times \frac{9}{4}+3$$

Multiply 2 and \frac{81}{16} to get \frac{81}{8}.

$$y=\frac{81}{8}-5\times \frac{9}{4}+3$$

Multiply -5 and \frac{9}{4} to get -\frac{45}{4}.

$$y=\frac{81}{8}-\frac{45}{4}+3$$

Subtract \frac{45}{4} from \frac{81}{8} to get -\frac{9}{8}.

$$y=-\frac{9}{8}+3$$

Add -\frac{9}{8} and 3 to get \frac{15}{8}.

$$y=\frac{15}{8}$$

The system is now solved.

$$y=\frac{15}{8} x=\frac{9}{4}$$