Investigate and explain the different number of solution and equations can have
Question 1.
Examine the six different equations that follow determine which equations have one solution no solution or infinitely many solutions.
Put a circle around the two equations that have infinite solutions.
Put a square around the two equations that have no Solution.
Underline the two equations that have one solution.
2×+3=2×+7
7×+3=7×+3
4×+22=8×+10
5×+5=5×+4
To determine the number of solutions for each equation, we need to simplify and analyze the expressions on each side of the equation.
1. 2x + 3 = 2x + 7
Subtracting 2x from both sides, we get:
3 = 7
Since this is a false statement, this equation has no solutions.
2. 7x + 3 = 7x + 3
This equation is an identity because both sides are equal, so it has infinitely many solutions.
3. 4x + 22 = 8x + 10
Subtracting 4x from both sides, we get:
22 = 4x + 10
Subtracting 10 from both sides:
12 = 4x
Dividing by 4:
x = 3
This equation has one solution.
4. 5x + 5 = 5x + 4
Subtracting 5x from both sides, we get:
5 = 4
Since this is a false statement, this equation has no solutions.
Therefore, the equations with one solution are 4x + 22 = 8x + 10 and the equations with infinitely many solutions are 7x + 3 = 7x + 3. The equations with no solutions are 2x + 3 = 2x + 7 and 5x + 5 = 5x + 4.