The system of two equations, 3x + 2y = 7 and 6x + 4y = 10 is consistent.Question 2Answera.Trueb.False

Break Down the Problem

1. We have a system of two equations:

   • Equation 1: $3x + 2y = 7$
   • Equation 2: $6x + 4y = 10$

2. We need to determine if this system is consistent. A system of equations is consistent if there is at least one set of values for $x$ and $y$ that satisfies both equations.

Relevant Concepts

1. A consistent system can be determined by checking if the two equations represent the same line or intersect at a point.

2. To check for consistency, we can manipulate the equations to see if they are equivalent.

Analysis and Detail

1. Let's manipulate Equation 1:

   • Multiply Equation 1 by 2: $2(3x + 2y) = 2(7) \implies 6x + 4y = 14$

2. Now we compare the modified Equation 1 with Equation 2:

   • Modified Equation 1: $6x + 4y = 14$
   • Equation 2: $6x + 4y = 10$

3. Since $6x + 4y = 14$ and $6x + 4y = 10$ are not the same, the system of equations does not have a solution.

Verify and Summarize

1. The equations are not equivalent and thus do not represent the same line.
2. Because they don’t intersect at any point, the system is inconsistent.

Final Answer

The answer is b. False; the system of equations is not consistent.