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The solution to a system of equations is (2,-4).one equation in the system is 2x+y=0.explain how you can find a second equation for the system.then find a second equation.solve by system of equations to justify your answer

Answer :

The second equation is 3x + y = 2.

Let the other equation be of the form ax + by = c, where a, b and c are constants.

Given equation is 2x + y = 0

We have, a₁ = 2 and a₂ = 1

And b₁ = a and b₂ = b

Since, both equations have a unique solution,

∴ a₁ ÷ b₁ ≠ a₂ ÷ b₂

2 ÷ a ≠ 1 ÷ b

2b ≠ a                                               … (1)

                         

Also, (2, -4) is the solution of the equations, so it will satisfy the equations

2a - 4b = c

b = (2a - c)/4

Let c=2

b = (2a - 2) ÷ 4

b = 1

Now we can take any value for a and b which satisfy eq.(1)

Let a=3

b = (2(3) - 2) ÷ 4

b = 1

Thus, a = 3 and b=1 satisfy eq.(1)

Hence the second equation is 3x + y = 2

The equations are justified by keeping the values -

2x+y=0                               ... (2)

3x+y=2                             ... (3)

From eq.(2),

y=-2x

Putting value of y in eq. (3), we get,

3x+(-2x)=2

3x-2x=2

x=2

Now, putting x=2 in eq.(2)

2(2)+y=0

y=-4

Hence, the solution is justified.

Know more about Linear Equation with two variables: https://brainly.com/question/24085666

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