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Q: What are the solutions to the simultaneous equations of x squared plus y squared equals 20 and 2y minus x equals 0?

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They are: (3, 1) and (-11/5, -8/5)

If: 2x+y = 5 and x2-y2 = 3 Then the solutions work out as: (2, 1) and ( 14/3, -13/3)

The two rational solutions are (0,0,0) and (1,1,1). There are no other real solutions.

Through a process of elimination and substitution the solutions are s = 8 and x = 5

These are two expressions, not equations. Expressions do not have solutions, only equations do. NB equations include the equals sign.

They are simultaneous equations and their solutions are x = 41 and y = -58

1st equation: x^2 -xy -y squared = -11 2nd equation: 2x+y = 1 Combining the the two equations together gives: -x^2 +3x +10 = 0 Solving the above quadratic equation: x = 5 or x = -2 Solutions by substitution: (5, -9) and (-2, 5)

Simultaneous suggests at least two equations.

Do you mean: 4x+7y = 47 and 5x-4y = -5 Then the solutions to the simultaneous equations are: x = 3 and y = 5

Merge the equations together and form a quadratic equation in terms of x:- 3x2-20x+28 = 0 (3x-14)(x-2) = 0 x = 14/3 or x = 2 So when x = 14/3 then y = -13/3 and when x = 2 then y = 1

Simultaneous equations.

I notice that the ratio of the y-coefficient to the x-coefficient is the same in both equations. I think that's enough to tell me that their graphs are parallel. So they don't intersect, and viewed as a pair of simultaneous equations, they have no solution.

The solutions work out as: x = 52/11, y = 101/11 and x = -2, y = -11

The system is simultaneous linear equations

x = -3 y = -2

Another straight line equation is needed such that both simultaneous equations will intersect at one point.

0 = 0 is an identity and not an equation. Equations have solutions, identities do not.

Simultaneous equations: x/3 -y/4 = 0 and x/2 +3y/10 = 27/5 Multiply all terms in the 1st by 12 and in the 2nd equation by 10 So: 4x -3y = 0 and 5x +3y = 54 Add both equations together: 9x = 54 => x = 6 Solutions by substitution: x = 6 and y = 8

They are called the solutions or roots of the equations.

It works out that the solutions are: x = 3 and y = 2

They are two equations in two unknown variables (x and y), which are inconsistent. That is to say, there is no simultaneous solution. An alternative approach is to say that they are the equations of two lines in the Cartesian plane. The lines are parallel and so they do not meet indicating that there is no simultaneous solution.

Equations: 3x-5y = 16 and xy = 7 Solutions: (7, 1) and (-5/3, -21/5)

The quadratic equation will have two solutions.

The points of intersection of the equations 4y^2 -3x^2 = 1 and x -2 = 1 are at (0, -1/2) and (-1, -1)

The equations are identical in value, ie the second is merely twice the first...

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