No solution:
2x+3+2x+7
7x+3+7x+3
1Consider the two equations you put a square around, which form a system with no solution.
2.Solve the equations.
3.What do you notice about these equations?
4.What does it mean to have no solution?
5.Plug a few points into the original equations and check to show that they can have no solution.
Explain your work.
1. 2x+3+2x+7=7x+3+7x+3
4x+10=14x+6 (Combine like terms)
10=10x+6 (Subtract 4x from both sides)
4=10x (Subtract 6 from both sides)
4/10=x (Divide by 10)
x=2/5
2. By solving the equations, we find that x=2/5.
3. These equations are parallel lines with the same slope but different y-intercepts.
4. Having no solution means that the lines represented by the equations are parallel and will never intersect, indicating that there is no common solution for the equations.
5. Let's plug in the point x=2/5 into both equations:
- For the first equation, 2(2/5) + 3 + 2(2/5) + 7 = 4/5 + 3 + 4/5 + 7 = 8/5 + 4/5 + 7 = 12/5 + 7
- For the second equation, 7(2/5) + 3 + 7(2/5) + 3 = 14/5 + 3 + 14/5 + 3 = 28/5 + 6
Since 12/5 + 7 does not equal 28/5 + 6, this confirms that there is no common solution for these equations.