If: 2x+y = 1 then y = 1-2x
If: x^2 -xy -y^2 = -11 then x^2 -x(1-2x) -(1-2x)^2 -11 = 0
Multiplying out the brackets: x^2 -x+2x^2 -1+4x -4x^2+11 = 0
Collecting like terms: -x^2+3x+10 = 0
Solving the above quadratic equation: x = 5 or x = -2
Solutions by substitution: when x = 5 then y = -9 and when x = -2 then y = 5
24
many solutions
This quadratic equation has no solutions because the discriminant is less than zero.
Two solutions and they are:- x = 0 and y = 3
1
It is a quadratic equation with no real roots or real solutions. In the complex domain, the solutions are 1 +/- i where i is the imaginary square root of -1.
The two solutions are the conjugate complex numbers, +i*sqrt(11) and -i*sqrt(11), where i is the imaginary square root of -1.
many solutions
There are 120 solutions.
24
This quadratic equation has no solutions because the discriminant is less than zero.
There are four solutions to 9x4 plus 27x3 - 4x2 - 12x equals 0. One of the solutions is x = -3.
Two solutions and they are:- x = 0 and y = 3
If: 3x+2y = 5x+2y = 14 Then: 3x+2y = 14 and 5x+2y =14 Subtract the 1st equation from the 2nd equation: 2x = 0 Therefore by substitution the solutions are: x = 0 and y = 7
zero solutions. If you plot these two lines, you will see that they are parallel and do not intersect.
1 solution
1