4x+22=8x+10 5x+5=5x+4
Question 3: No Solutions
Consider the two equations you put a square around, which form a system with no
solution. Solve the equations
For the first equation:
4x + 22 = 8x + 10
Subtracting 4x from both sides:
22 = 4x + 10
Subtracting 10 from both sides:
12 = 4x
Dividing both sides by 4:
x = 3
Now let's look at the second equation:
5x + 5 = 5x + 4
Subtracting 5x from both sides:
5 = 4
This is a contradiction, indicating that there is no solution to this system of equations.
To solve the system of equations:
Equation 1: 4x + 22 = 8x + 10
Equation 2: 5x + 5 = 5x + 4
Let's start by solving Equation 1:
Subtract 4x from both sides to isolate the constant term:
22 = 4x + 8x + 10
Combine like terms:
22 = 12x + 10
Subtract 10 from both sides:
12 = 12x
Divide both sides by 12:
x = 1
Now, let's solve Equation 2:
Subtract 5x from both sides to isolate the constant term:
5 = 5x + 4 - 5x
Combine like terms:
5 = 4
This is where we encounter a contradiction. The equation 5 = 4 is false, which means the system of equations has no solution.
Therefore, the answer to the system of equations is "No Solutions".
To solve the system of equations with no solution, let's analyze the first equation:
4x + 22 = 8x + 10
To get rid of the variables on one side, we can subtract 4x from both sides:
22 = 4x + 10
Next, subtract 10 from both sides:
12 = 4x
Now, divide both sides by 4 to isolate x:
x = 12/4
x = 3
So, the solution for the first equation is x = 3.
Now, let's move on to the second equation:
5x + 5 = 5x + 4
In this equation, we can observe that both sides contain the same variable (5x) and the same constant term (5). Therefore, we can conclude that both sides of the equation are equal.
Since both sides are equal, this equation is true for any value of x. Thus, there are infinitely many solutions for the second equation.
To summarize, the first equation has a solution x = 3, and the second equation has infinitely many solutions.