What was the purpose of the coordinate graphing system described by descartes in his book discourse on method?

a. to use algebraic methods to solve geometric problems.
b. to prove the universe was sun-centered.
c. to represent equations for the queen of sweden.
d. to prove his own existence.

A. To use algebraic methods to solve geometric problems.

Step-by-step explanation:

Descartes, a French mathematician and a philosopher, explained what is  the system of Cartesian Coordinates. In Descartes's system of coordinates, geometry and algebra were united for the first time to create which known as analytic geometry .

Cartesian coordinates are used to plot a point in expanse by giving its respective distance from perpendicular intersecting lines named as x axis and y axis. In coordinate geometry all points, lines, and figures can be drawn in a coordinate plane by references of both the axes.

i think it is c, not positive though

step-by-step explanation:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.