Question

Solve the system of linear equations using linear combination

3a + 6b = 45
2a - 2b = -12
Which is the solution to the system?

Answer 1

(-3, 3)

Explanation:

Let's solve this system using elimination through addition and subtraction.

Notice that if we multiply 2a - 2b = -12 by 3, we get 6a - 6b = -36, which cancels out the +6b in 3a + 6b = 45:

3a + 6b = 45

-6a - 6b = -36

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-3a = 9. Thus, a = -9/3, or a = -3.

Subbing -3 for a in the second equation, to find b, we get:

2(-3) - 2b = -12, or

-6 - 2b = -12, or -2b = -6. Thus, b = 3.

The solution is (-3, 3).

Next time, would you please share the possible answer choices.