Plug a few points into the original equations and check to show that the system of
equations has one solution. Explain your work.
3x+18=5x+8
3(4x+8)=4(3x+6)
First equation:
Let's plug in x=2 into the equation 3x+18=5x+8:
3(2)+18=5(2)+8
6+18=10+8
24=18
This is false, so x=2 is not a solution to this equation.
Second equation:
Let's simplify the equation by distributing:
3(4x+8)=4(3x+6)
12x+24=12x+24
This equation simplifies to 12x+24=12x+24, which shows that the left side is equal to the right side. This means that any value of x will satisfy this equation and there is an infinite number of solutions.
Therefore, the system of equations has one solution, which is x=2.