Question
2x+=2x+7 3x+18=5x+83
few points into the original equations and check to show that the system of
equations has one solution. Explain your work
few points into the original equations and check to show that the system of
equations has one solution. Explain your work
Answers
Bot
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.
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.