Question

Solve the system of equations below graphically.
X=2-y
y=x² – 4

A) (0, -4)
B) (1.5, 0) and (-3,5)
C) (2,0) and (-2,5)
D) (2,0) and (-3,5)​

Answer 1

Option D: $(2,0) \text { and }(-3,5)$ is the solution to the system of equations.

Explanation:

Given that the system of equations are $x=2-y$ and $y=x^{2} -4$

We need to determine the solution to the system of equations graphically.

Let us consider plotting the equation $x=2-y$ in the graph.

First, we shall determine the x and y intercepts for the equation $x=2-y$

When $x=0$, we get,

$0=2-y$

$2=y$

Similarly, when $y=0$, we get,

$x=2-0$

$x=2$

Thus, let us join the coordinates $(0,2)$ and $(2,0)$ to get the equation of the line.

Let us consider plotting the equation $y=x^{2} -4$ in the graph.

When $x=0$ ⇒ $y=-4$

When $y=0$ ⇒ $x=\pm2$

Thus, let us join the coordinates $(0,-4)$, $(2,0)$ and $(-2,0)$ to get the equation of the parabola.

The solution of the two equations is the point of intersection of these two lines.

Hence, the lines intersect at the points $(2,0) \text { and }(-3,5)$

Therefore, Option D is the correct answer.

The image of the solution is attached below: