If: 2x+y = 1 then y = 1-2x
If: x^2+xy+y^2 = 7 then x^2+x(1-2x)+(1-2x)^2-7 = 0
So: x^2+x-2x^2+1-4x+4x^2-7 = 0
Collecting like terms: 3x^2-3x-6 = 0 => x^2-x-2 = 0
Solving the above quadratic equation: x = -1 or x = 3
Solutions by substitution: when x = -1 then y = 3 and when x = 2 then y = -3
The solutions are: x = 4, y = 2 and x = -4, y = -2
No. It's a quadratic equation, and it has two solutions.
These are two expressions, not equations. Expressions do not have solutions, only equations do. NB equations include the equals sign.
2.
-x2+2.5x+1=0 x=-0.350781 x=2.85078
x = -½
The solutions are: x = 4, y = 2 and x = -4, y = -2
No. It's a quadratic equation, and it has two solutions.
It has no solutions because the discriminant is less than zero.
If: 2x+y = 5 and x2-y2 = 3 Then the solutions work out as: (2, 1) and ( 14/3, -13/3)
These are two expressions, not equations. Expressions do not have solutions, only equations do. NB equations include the equals sign.
104
2.
-x2+2.5x+1=0 x=-0.350781 x=2.85078
It is a quadratic equation and its solutions are: x = 4 or x = -9
(2x + 1)(2x + 1) or (2x + 1)2 so x = -0.5
89