The two equations are:
1) 3xy - y² = 8
2) x - 2y = 1
Make x the subject of (2):
x - 2y = 1 → x = 2y + 1
substitute for x in (1) and solve for y:
3xy - y² = 8
→ 3(2y + 1)y - y² = 8
→ 6y + 3y - y² - 8 = 0
→ 5y + 3y - 8 = 0
→ (5y + 8)(y - 1) = 0
→ 5y + 8 = 0 → y = -8/5
or y - 1 = 0 → y = 1
and substitute into 2 to find the corresponding x:
y = -8/5 → x = 2(-8/5) + 1 = -11/5
y = 1 → x = 2(1) + 1 = 3
→ the solutions are the ordered pairs (-11/5, -8/5) {or (-2.2, -1.6)} and (3, 1)
The solutions work out as: x = 52/11, y = 101/11 and x = -2, y = -11
It is a simultaneous equation and its solution is x = -1 and y = -5
Add the two equations together. This will give you a single equation in one variable. Solve this - it should give you two solutions. Then replace the corresponding variable for each of the solutions in any of the original equations.
How many solutions are there to the following system of equations?2x - y = 2-x + 5y = 3if this is your question,there is ONLY 1 way to solve it.
Solving these simultaneous equations by the elimination method:- x = 1/8 and y = 23/12
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)
The two rational solutions are (0,0,0) and (1,1,1). There are no other real solutions.
These are two expressions, not equations. Expressions do not have solutions, only equations do. NB equations include the equals sign.
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)
Through a process of elimination and substitution the solutions are s = 8 and x = 5
They are simultaneous equations and their solutions are x = 41 and y = -58
Simultaneous suggests at least two equations.
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
Do you mean: 4x+7y = 47 and 5x-4y = -5 Then the solutions to the simultaneous equations are: x = 3 and y = 5
Simultaneous equations.