Question

What is the solution to the following system of equations?

2 x + 3y = 24
6x + 9 y = 36
A)F (3, 6)
B)G (21, -6)
C)H All real numbers
D)J No real solution

Answer 1

The two equations in the system are not independent but multiples of each other, indicating that they represent the same line. Therefore, they do not have a unique solution; instead, they have infinitely many solutions, so the correct answer is C) H All real numbers.

Step-by-step explanation:

The solution to the given system of equations can be determined by analyzing the relationship between the two equations. The first equation is 2x + 3y = 24 and the second is 6x + 9y = 36. If we observe carefully, the second equation is exactly three times the first equation. This implies that the two equations are not independent but the same line, so every point on the line determined by the first equation will also satisfy the second equation.

Therefore, the system does not have a unique solution; instead, it has infinitely many solutions. Every pair (x, y) that satisfies the first equation will also satisfy the second. Consequently, the correct answer is C) H All real numbers since any point on this line represents a solution to the system of equations.

Answer 2

The system of equations 2x + 3y = 24 and 6x + 9y = 36 represents the same line and therefore has an infinite number of solutions, so the correct answer is C)H All real numbers.

Step-by-step explanation:

The system of equations provided is 2x + 3y = 24 and 6x + 9y = 36. This is a system of linear equations which can be solved by various methods such as substitution, elimination, or graphing. Observing these equations, we notice that the second equation is simply the first equation multiplied by 3. This implies that the two equations are actually the same line, therefore they have an infinite number of solutions as every point on the line satisfies both equations. So the correct answer is C)H All real numbers.