Consider the equations [ 3x + 18 =5x + 8 ], which form a system with no
solution.
What do you notice about these equations?
What does it mean to have no solutions?
Plug a few points into the original equations and check to show that they can have no
solution. Explain your work.
Looking at the given equations, we see that they have different constants on the right side (18 and 8) and different coefficients for x (3 and 5). This means that when we try to solve for x, we will not be able to find a single value that satisfies both equations.
Having no solutions means that there is no value of x that can make both equations true at the same time. This implies that the two lines represented by the equations are parallel and will never intersect.
Let's plug in a few points into the original equations to confirm that they have no solution:
1. For x = 0:
3(0) + 18 = 18 ≠ 5(0) + 8 = 8
2. For x = 1:
3(1) + 18 = 21 ≠ 5(1) + 8 = 13
3. For x = 2:
3(2) + 18 = 24 ≠ 5(2) + 8 = 18
In each case, the left side of the equation does not equal the right side, confirming that there is no solution to the system of equations.