Question

Являются ли решением системы уравнений х+у=1 4х+2у=6 пара чисел: а) (2;-1) б) (-1;2) в) (2;1) ответ с решением! Спасибо,заи)0

Answer 1

X+y=1
4x+2y=6
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x+y=1
2x+y=3
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(2x+y)-(x+y)=3-1
2x-x+y-y=2
x=2
===
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y=1-x, y=1-2, y=-1
                     =====
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/x,y/=/2,-1/
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Answer 2

Solution for the System of Equations:

The given system of equations is: 1. \(x + y = 1\) 2. \(4x + 2y = 6\)

To check if a given pair of numbers is a solution to the system, we can substitute the values of \(x\) and \(y\) from each pair into the equations and see if they satisfy both equations.

Let's evaluate each pair:

Pair (2, -1):

Substituting \(x = 2\) and \(y = -1\) into the equations: 1. \(2 + (-1) = 1\) 2. \(4*2 + 2*(-1) = 6\)

Both equations are satisfied, so the pair (2, -1) is a solution to the system of equations.

Pair (-1, 2):

Substituting \(x = -1\) and \(y = 2\) into the equations: 1. \(-1 + 2 = 1\) 2. \(4*(-1) + 2*2 = 6\)

Both equations are not satisfied, so the pair (-1, 2) is not a solution to the system of equations.

Pair (2, 1):

Substituting \(x = 2\) and \(y = 1\) into the equations: 1. \(2 + 1 = 1\) 2. \(4*2 + 2*1 = 6\)

The first equation is not satisfied, so the pair (2, 1) is not a solution to the system of equations.

Therefore, the only pair that is a solution to the given system of equations is (2, -1).