Question

What is the solution to the system of equations?

Use the linear combination method.

3x+4y=1
4x+5y=0

Answer 1

x = -5

y = 4

Explanation:

3x + 4y = 1 /*(-4)

4x + 5y = 0 /*3

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-12x - 16y = -4

12x + 15y = 0 +

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-y = -4

y = 4

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12x = -15y

12x = -60

x = -5

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Answer 2

Answer: x = - 5

y = 4

Explanation:

The given system of linear equations is expressed as

3x + 4y = 1- - - - - - - - - - - - -1

4x + 5y = 0- - - - - - - - - - - -2

We would eliminate x by multiplying equation 1 by 4 and equation 2 by 3. It becomes

12x + 16y = 4- - - - - - - - - - -3

12x + 15y = 0- - - - - - - - - - - -4

Subtracting equation 4 from equation 3, it becomes

y = 4

Substituting y = 4 into equation 1, it becomes

3x + 4 × 4 = 1

3x + 16 = 1

Subtracting 16 from the left hand side and the right hand side of the equation, it becomes

3x + 16 - 16 = 1 - 16

3x = - 15

Dividing the left hand side and the right hand side of the equation by 3, it becomes

3x/3 = - 15/3

x = - 5