If: x = 2y-2 and x^2 = y^2+7
Then: (2y-2)^2 = y^2+7 => 4y^2-8y+4 = y^2+7 => 3y^2-8y-3= 0
Solving the above quadratic equation: y = -1/3 or y = 3
Solutions by substitution: when y=-1/3 then x=-8/3 and when y=3 then x=4
Since the first equation is already solved for "x", you can replace "x" by "2y-2" in the second equation and continue from there.
The solutions are: x = 4, y = 2 and x = -4, y = -2
They are: (3, 1) and (-11/5, -8/5)
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)
These are two expressions, not equations. Expressions do not have solutions, only equations do. NB equations include the equals sign.
Four.
The solutions are: x = 4, y = 2 and x = -4, y = -2
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)
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)
These are two expressions, not equations. Expressions do not have solutions, only equations do. NB equations include the equals sign.
The two rational solutions are (0,0,0) and (1,1,1). There are no other real solutions.
Four.
4
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
If: x = 2y-2 and x^2 = y^2+7 Then: (2y-2)^2 = y^2+7 So: (2y-2)(2y-2) = y^2+7 It follows: 4y^2-y^2-8y+4-7 = 0 => 3y^2-8y-3 = 0 Solving the above quadratic equation: y = -1/3 or y = 3 Solutions: when y = 3 then x = 4 and when y = -1/3 then x = -8/3
If you mean: x2+2x+1 = 0 then it is a quadratiic equations whose solutions are equal because x = -1 and x = -1
I suggest you solve the second equation for one of the variables, then replace that in the first equation.Another Answer:-x2+xy+y2 = 7 and 2x+y = 1Merging the two equations together in terms of x will result in a quadratic equation of:3x2-3x-6 = 0Divide all terms by 3:x2-x-2 = 0When factored: (x+1)(x-2) = 0So: x = -1 or x = 2Solutions: when x = -1 then y = 3 and when x = 2 then y = -3