\left\{ \begin{array} { l } { y = - x ^ { 2 } + 2 x + 3 } \\ { x = \frac { 3 } { 2 } } \end{array} \right.
Solve for y, x
x = \frac{3}{2} = 1\frac{1}{2} = 1.5
y = \frac{15}{4} = 3\frac{3}{4} = 3.75
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y=-\left(\frac{3}{2}\right)^{2}+2\times \frac{3}{2}+3
Consider the first equation. Insert the known values of variables into the equation.
y=-\frac{9}{4}+2\times \frac{3}{2}+3
Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.
y=-\frac{9}{4}+3+3
Multiply 2 and \frac{3}{2} to get 3.
y=\frac{3}{4}+3
Add -\frac{9}{4} and 3 to get \frac{3}{4}.
y=\frac{15}{4}
Add \frac{3}{4} and 3 to get \frac{15}{4}.
y=\frac{15}{4} x=\frac{3}{2}
The system is now solved.
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