is it possible for system of two linear equations to have no solution.
Yes, the slope of both lines is 0.5, which means the lines really are parallel. They never intersect, so there is no point that lies on both lines, and no solution to the system.
Yes, it is possible for a system of two linear equations to have no solution. This occurs when the two lines represented by the equations are parallel and never intersect.
To determine whether a system of two linear equations has a solution or not, we need to compare the slopes of the lines and the y-intercepts.
The standard form of a linear equation is:
Ax + By = C,
where A, B, and C are constants, and x and y are variables.
Let's consider a system of two linear equations:
Equation 1: A1x + B1y = C1,
Equation 2: A2x + B2y = C2.
If the slopes of the two lines represented by these equations are equal (A1/B1 = A2/B2) and the y-intercepts are different (C1/B1 ≠ C2/B2), then the lines are parallel, and the system of equations has no solution.
In this case, the lines will never intersect, and there will be no common solution for both equations in the system.
It's important to note that if the slopes are equal and the y-intercepts are also equal (C1/B1 = C2/B2), the two lines are coincident or overlapping, and the system of equations will have infinitely many solutions.