If a system of equations consists of two parallel lines, then how many solutions does it have? 0 solutions
1 solution
infinitely many solutions

The system of equations consists of two parallel lines has no solution

Solution:

When a system of equations consists of two parallel lines, then it has no solution

If the two lines are parallel, then they will never meet.

If the two linear equations have the same slope and different y-intercepts, then the lines will be parallel.

Since parallel lines never intersect, a system composed of two parallel lines will have no solution

Consider the system of equations

y = -3x + 9 -- eqn 1

y = -3x - 7 --- eqn 2

The above system of equations are parallel lines, so they have no solution

Substitute eqn 2 in eqn 1

-3x - 7 = -3x + 9

-3x + 3x = 9 + 7

The  coefficients are the same on both sides ,then the sides will not equal, therefore no solution occurs

This means there are no coordinates (x, y) that satisfy both equations at the same time. This means there is is no point P = (x, y) that can lie on both lines at the same time.

So the system of equations consists of two parallel lines has no solution

x is variable or an unknown value to find

example:

2x = 5 which means x = 3