What does it mean to have no solutions?
5 answers
Having no solutions means that there are no values or answers that satisfy a particular equation, problem, or condition. It indicates that there is not a valid solution within the given context or parameters. In mathematics, for example, if an equation has no solutions, it implies that the equation cannot be true for any value of the variable.
Consider the two equations that you underlined, which form a system with one
solution. Solve the equations. 3x+18=5x+8
3(4x8)=4(3x+)
solution. Solve the equations. 3x+18=5x+8
3(4x8)=4(3x+)
To solve the system of equations:
Equation 1: 3x + 18 = 5x + 8
Equation 2: 3(4x + 8) = 4(3x + ?)
First, let's solve Equation 1:
Rearrange the equation by isolating the variable terms on one side:
3x - 5x = 8 - 18
-2x = -10
Divide both sides of the equation by -2 to solve for x:
x = -10 / -2
x = 5
Now that we have the value of x, we can substitute it into Equation 2 to find the value for the second variable:
3(4x + 8) = 4(3x + ?)
3(4(5) + 8) = 4(3(5) + ?)
3(20 + 8) = 4(15 + ?)
3(28) = 4(15 + ?)
84 = 60 + 4?
Subtract 60 from both sides of the equation:
84 - 60 = 4?
24 = 4?
Divide both sides by 4 to solve for ?:
? = 24 / 4
? = 6
Therefore, the solution for the system of equations is x = 5, ? = 6.
Equation 1: 3x + 18 = 5x + 8
Equation 2: 3(4x + 8) = 4(3x + ?)
First, let's solve Equation 1:
Rearrange the equation by isolating the variable terms on one side:
3x - 5x = 8 - 18
-2x = -10
Divide both sides of the equation by -2 to solve for x:
x = -10 / -2
x = 5
Now that we have the value of x, we can substitute it into Equation 2 to find the value for the second variable:
3(4x + 8) = 4(3x + ?)
3(4(5) + 8) = 4(3(5) + ?)
3(20 + 8) = 4(15 + ?)
3(28) = 4(15 + ?)
84 = 60 + 4?
Subtract 60 from both sides of the equation:
84 - 60 = 4?
24 = 4?
Divide both sides by 4 to solve for ?:
? = 24 / 4
? = 6
Therefore, the solution for the system of equations is x = 5, ? = 6.
3(4x + 8) = 4(3x +6)
To solve the equation 3(4x + 8) = 4(3x + 6), we can follow these steps:
1. Distribute the coefficients:
12x + 24 = 12x + 24
2. Simplify the equation:
Both sides of the equation are identical, so they are equal.
In this case, the equation simplifies to 12x + 24 = 12x + 24.
When this occurs, it means that both sides of the equation are equivalent and will cancel out each other. Therefore, we do not have a unique solution in this case.
In conclusion, this equation has infinitely many solutions or no unique solution.
1. Distribute the coefficients:
12x + 24 = 12x + 24
2. Simplify the equation:
Both sides of the equation are identical, so they are equal.
In this case, the equation simplifies to 12x + 24 = 12x + 24.
When this occurs, it means that both sides of the equation are equivalent and will cancel out each other. Therefore, we do not have a unique solution in this case.
In conclusion, this equation has infinitely many solutions or no unique solution.
1 answer