Question

Which equations can be used in a system of equations to solve for the unknowns? Check all that apply.

A = 2
-6A + B = 2
3A - B + C = 1
B = 0
9A - 3B + C = 1

Answer 1

To solve the system of equations, use B=0 to simplify 3A - B + C = 1 into 3A + C = 1. Since A=2 is given, substitute it in to find C=-5. The solution to the system is A=2, B=0, C=-5.

Step-by-step explanation:

To solve for the unknowns using a system of equations, you need to check which equations can be combined to eliminate variables and find the solutions step-by-step. Given the system:

• A = 2
• -6A + B = 23
• 3A - B + C = 1
• B = 0
• 9A - 3B + C = 1

From the list above, it's clear that the equation B = 0 already gives us a known value for B. Using this known value, we can substitute B=0 into the third equation, 3A - B + C = 1, which simplifies to 3A + C = 1. Now, we have two equations with only two unknowns (A and C), because we were already given that A=2:

• A = 2
• 3A + C = 1 (with B substituted)

We can now solve for C using these two equations:

1. Identify the unknown: C
2. Identify the knowns: A=2, B=0
3. Choose an equation: 3A + C = 1
4. Plug in the knowns and solve for the unknown: 3(2) + C = 1, which simplifies to 6 + C = 1, resulting in C = -5