Question

7x+3=7x+3 3(4x+8)=4(3x+6)

one point into the original equations and check to show that the equations can have more than one solution. Explain your work.

Answer 1

Given the two equations:

1) 7x + 3 = 7x + 3
2) 3(4x + 8) = 4(3x + 6)

First, let's simplify the second equation:

3(4x + 8) = 4(3x + 6)
12x + 24 = 12x + 24

Now, let's analyze both equations:

1) 7x + 3 = 7x + 3
This equation is true for any value of x, because both sides of the equation are the same. Therefore, this equation has infinitely many solutions, as any value of x will satisfy the equation.

2) 12x + 24 = 12x + 24
This equation is also true for any value of x, because both sides of the equation are the same. Therefore, this equation also has infinitely many solutions, as any value of x will satisfy the equation.

Since both equations have infinitely many solutions and are true for any value of x, we can choose any point (x, y) to check if it satisfies both equations.

Let's choose x = 1:

1) 7(1) + 3 = 7(1) + 3
7 + 3 = 7 + 3
10 = 10

2) 12(1) + 24 = 12(1) + 24
12 + 24 = 12 + 24
36 = 36

The point (x = 1, y = 10) satisfies both equations, proving that the two equations can have more than one solution. In fact, these equations have infinitely many solutions because they hold true for any value of x.