# How many solutions are in a linear circle system?

## How many solutions are in a linear circle system?

There are three possible types of solutions to a system of equations representing a circle and a line: (1) no solution, the line does not intersect the circle; (2) one solution, the line is tangent to the parabola; (3) two solutions, the line intersects the circle in two points. See (Figure).

### How is the equation of a circle related to quadratics?

A quadratic relation containing the square of both the x-variable and the y-variable (with their coefficients being one, or the same value) is a circle. (x – h)2 + (y – k)2 = r2 where the center of the circle is the point (h,k), and the radius is r.

#### What is a linear simultaneous equation?

Both equations having to same variable i.e., x, y) Simultaneous linear equations: Two linear equations in two variables taken together are called simultaneous linear equations. The solution of system of simultaneous linear equation is the ordered pair (x, y) which satisfies both the linear equations.

What is a linear equation in 2 variables?

Linear equations in two variables. If a, b, and r are real numbers (and if a and b are not both equal to 0) then ax+by = r is called a linear equation in two variables. (The “two variables” are the x and the y.) The numbers a and b are called the coefficients of the equation ax+by = r.

How many solutions are there for linear equations in two variables?

Further, a linear equation in two variables has infinitely many solutions. The graph of every linear equation in two variables is a straight line and every point on the graph (straight line) represents a solution of the linear equation.

## How to solve a system of simultaneous linear equations?

The solution of system of simultaneous linear equations is the ordered pair (x,y) if the set has two linear equations and (x,y,z….) if it has more linear equations. Simultaneous linear equations with 2 variables Example 1: { 3 x − y = 1 x + y = 3 Methods for solving simultaneous linear equation