2x+=2x+7 3x+18=5x+83

Question

few points into the original equations and check to show that the system of
equations has one solution. Explain your work

Answer 1

Let's first solve the system of equations to find the solution:

1) 2x + 2x = 2x + 7
Combining the 2x terms, we get:
4x = 2x + 7
Now, subtract 2x from both sides:
2x = 7
Now, divide by 2:
x = 7/2 = 3.5

Now, substitute the value of x found in the second equation:

2) 3x + 18 = 5x + 83
Substituting x = 3.5, we get:
3(3.5) + 18 = 5(3.5) + 83
Now evaluate:
10.5 + 18 = 17.5 + 83

Combining the numbers, we get:
28.5 = 100.5

Now, subtract 28.5 from both sides to check if they are equal:
100.5 - 28.5 = 72 ≠ 0

Since both sides are not equal, the system of equations does NOT have one solution. There must be an error in one of the equations, or it's not a valid system to solve.