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What is the solution to this system of equations using the linear combination method?5x + y = 24x + y = 5A: (-2, 12)B: (0, 2)C: (1, -8)D: (-3, 17)

User Ingmar
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1 Answer

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Step 1: Arrange the equations with like terms in columns

5x + y = 2

4x + y = 5

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Step 2: One set of coefficients shouls be opposites. In our case, we multiply the second equation by - 1

5x + y = 2

-4x - y = - 5 (Multiplied by - 1)

Step 3: We add the like terms

5x + - 4x = 5x - 4x = x

+y + - y = y - y = 0

2 + - 5 = 2 - 5 = -3

Important: please be careful with the negative and positive signs

Step 4: Solve for x

x = - 3

Step 5 : Solve for y in any of the equations, replacing x

5x + y = 2

5 * - 3 + y = 2

-15 + y = 2

y = 2 + 15

y = 17

Step 6: We write the solution as an ordered pair

(-3, 17)

User Vlince
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