Calculate the coordinates of the points of the intersection of the parabola y = x ^ 2-10 and the line y = 4x + 11

In order to find the coordinates of the intersection points of the parabola y = x ^ 2 – 10 and the straight line y = 4x + 11, we must solve a system of these equations.

System of equations:

y = x ^ 2 – 10;

y = 4x + 11.

We solve by substitution method.

x ^ 2 – 10 = 4x + 11;

y = 4x + 11.

We solve the first equation:

x ^ 2 – 4x – 10 – 11 = 0;

x ^ 2 – 4x – 21 = 0;

D = (-4) ^ 2 – 4 * 1 * (-21) = 16 + 84 = 100;

x1 = (4 + 10) / 2 = 7;

x2 = (4 – 10) / 2 = -3.

A set of systems:

System 1:

x1 = 7;

y2 = 4 * 7 + 11 = 28 + 11 = 39;

System 2:

x2 = -3;

y2 = 4 * (-3) + 11 = -12 + 11 = -1.

(7; 39) and (-3; -1).