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.
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.
1 answer
1 answer