Question

If $(a,b)$ is a solution to the system $\{\begin{array}{c}y=\frac{1}{2}x-2\\ y=-x^2+1\end{array}$ then the value of $b$ will be

• A. $-3$
• B. $-2$
• C. $1$
• D. $2$

Answer 1

The correct option is A $-3$

$y=\frac{1}{2}x-2$ and $y=-x^2+1$ ...Given

$\therefore 2y=x-4$ ....(1)

$\Rightarrow 2(-x^2+1)=x-4$

$\Rightarrow -2x^2+2=x-4$

$\Rightarrow 2x^2+x-6=0$

$\Rightarrow (2x-3)(x+2)=0$

$\Rightarrow x=\frac{3}{2}$ and $x=-2$

When $x=-2$, $y=-3$

Since $(a,b)$ is the solution of the given system of equations, we can say

$a=-2$ and $b=-3$