Question

Which is the best approximation of the solution shown on the linear-quadratic system graphed below?

Answer 1

(-1, 3)

Explanation:

The solution of a system of equations is the point where the two graphs intersect.

We can see in the picture that the point of intersection between the two graphs has an x-coordinate between -2 and 0 and y-coordinate between 2 and 3. In other words, the x-coordinate of the solution of the system lies in the interval [-2, 0], and the y-coordinate of the solution lies in the interval [2, 3]. Since both the third and fourth choices are outside both intervals, we can rule those two out. Which leaves us with (-2, 3) and (-1, 3).

As you can see in the attached picture, point (-1, 3) is much more close to the intersection of the two graphs than (-2, 3); therefore, we can conclude that (-1, 3) is the beast approximate solution of the linear-quadratic system.

Answer 2

The beast approximated solution of the linear-quadratic graph is (-1 , 3)

the second answer

Explanation:

* To solve this system of equation accurately

- You must have the equation of the parabola

- You must have the equation of the line

- You will solve them together by substitution method to find

the points of intersection between the parabola and the line

* But here we will try to find the approximated solution

∵ The point if intersection is between -1 and -2 as

x-coordinate nearest to -1

∵ The point if intersection is between 2 and 3 as

y-coordinate nearest to 3

∴ The best solution is (-1 , 3)

* The beast approximated solution of the linear-quadratic graph is (-1 , 3)