The first equation, 7x + 3 = 7x + 3, is an identity. This means that the equation is true for all values of x. There are infinitely many solutions to this equation.
The second equation, 3(4x + 8) = 4(3x + 6), can be simplified:
12x + 24 = 12x + 24
When we subtract 12x from both sides and subtract 24 from both sides, we get:
0 = 0
This equation is also an identity, meaning it is true for all values of x. Therefore, there are infinitely many solutions to this equation as well.
In summary, both of the given equations form a system with infinitely many solutions.
Consider the two equations
7x+3=7x+3.
3(4x+8)=4(3x+6)
you circled, which form a system with infinite solutions. Solve the equations.
5 answers
what do you notice about these questions?
I notice that both equations are identity equations, which means that they are true for all values of x. This is why there are infinitely many solutions for both equations.
what does it mean to have infinite solutions?
Having infinitely many solutions means that there are an unlimited number of values of x that satisfy the equation. In other words, if you were to plug in any value for x, the equation would still be true. It indicates that the equations are not sufficient to determine a unique value for x. Instead, the solutions form a continuous range or a set of values.