2x+=2x+7 3x+18=5x+83
Question 4: One Solution
Consider the two equations that you underlined, which form a system with one
solution. Solve the equations.
The first equation, 2x + 7 = 2x can be simplified by subtracting 2x from both sides:
2x + 7 - 2x = 2x - 2x
This simplifies to 7 = 0, which is false. Therefore, there is no solution for the first equation.
The second equation, 3x + 18 = 5x + 83, can be solved by isolating the variable on one side:
3x - 5x = 83 - 18
-2x = 65
Dividing by -2 gives:
x = -32.5
Therefore, the system of equations does not have one solution, as the first equation is unsolvable and the second equation has one solution, x = -32.5.
To solve the system of equations 2x + 7 = 2x and 3x + 18 = 5x + 83 that you have underlined, we can start by simplifying each equation separately. Let's break it down step by step.
Equation 1: 2x + 7 = 2x
In this equation, we have the same term on both sides of the equation (2x). We can subtract 2x from both sides to simplify it further:
2x - 2x + 7 = 2x - 2x
0x + 7 = 0
Simplifying further, we have:
7 = 0
Since this equation results in a contradiction (7 cannot equal 0), we know that there is no solution for this equation.
Now let's move on to the second equation.
Equation 2: 3x + 18 = 5x + 83
In this equation, we have variables (x) on both sides of the equation. We can start solving it by combining like terms on both sides:
3x - 5x = 83 - 18
-2x = 65
To isolate x, we'll divide both sides of the equation by -2:
-2x / -2 = 65 / -2
x = -65 / 2
So, we've found the value of x in the second equation: x = -65 / 2.
However, since the first equation had no solution, the system as a whole also has no solution. Therefore, there is no common solution to both equations.
To solve the system of equations, we'll start with the first equation:
2x + 7 = 2x + 7
Since both sides of the equation are the same, this equation is true for all values of x.
Now let's move on to the second equation:
3x + 18 = 5x + 83
To solve for x, we'll start by simplifying the equation:
3x - 5x = 83 - 18
-2x = 65
Next, we'll isolate x by dividing both sides of the equation by -2:
x = 65 / -2
Simplifying further:
x = -32.5
So the solution to the system of equations is x = -32.5.