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What are the solutions to the simultaneous equations of x equals 2y -2 and x squared equals y squared plus 7 showing work and answers?
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
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How do you find the solutions of the simultaneous equations of 2x plus 5y equals 16 and -5x-2y equals 2 showing work in step by step stages?
1 If: 2x+5y = 16 and -5x-2y = 2 2 Then: 2*(2x+5y =16) and 5*(-5x-2y = 2) is equvalent to the above equations 3 Thus: 4x+10y = 32 and -25x-10y = 10 4 Adding both equations: -21x = 42 or x = -2 5 Solutions by substitution: x = -2 and y = 4
What are the solutions to the simultaneous equations of 7x -8y equals 9 and 11x plus 3y equals -17 showing work?
Equations: 7x-8y = 9 and 11x+3y = -17 Multiply all terms in the 1st equation by 11 and all terms in the 2nd by 7 So: 77x-88y = 99 and 77x+21y = -119 Subtract the 1st equation from the 2nd equation: 109y = -218 => y = -2 Through substitution the solutions are: x = -1 and y = -2
What are the solutions to the simultaneous equations of 3x -5y equals 16 and xy equals 7 showing work?
If: 3x-5y = 16 then -5y = 16-3x => y = -3.2+0.6x by dividing all terme by -5 If: xy = 7 then x(-3.2+0.6x) = 7 => -3.2x+0.6x2 -7 = 0 Solving the quadratic equation: x = 7 or x = -5/3 Solutions of the equations by substitution are: x = 7, y = 1 and x = -5/3, y = -21/5
What are the solutions to the simultaneous equations of 6.6x plus 16.5y equals 52.8 and -16.5x -6.6y equals 6.6 showing key stages of work?
Eqn (A): => 2x + 5y = 16 Eqn (B): => 5x + 2y = -2 5*Eqn (A) - 2*Eqn (B): 21y = 84 => y = 4 Substituting for y in Eqn (a): x = -2
What are two types of non ideal solutions?
They are two types of Non-Ideal solutions. They are (i) Non-Ideal solutions showing positive deviation (ii) Non-ideal solutions showing negative deviation
What are the solutions to the simultaneous equations of x -2y equals 1 and 3xy -y squared equals 8 showing all appropiate work with answers?
If: x-2y = 1 and 3xy -y^2 = 8 Then: x = 1+2y and 3(1+2y)y -y^2 = 8 Hence: 3y+6y^2 -y^2 = 8 => 5y^2 +3y -8 = 0 Solving the above quadratic equation: y =1 or y = -8/5 Solutions by substitution are: when y=1 then x=3 and when y=-8/5 then x=-11/5
What are the solutions to the simultaneous equation of 3x plus 2y equals 5x plus 2y equals 14 showing work?
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
What is complete ionic equations?
An equation showing all dissolved compounds as ions
What is 5 divided by 312 showing work answers?
0.016
How are graphs and equations related?
The graph of an equation represents the solution set of the equation, that is all the solutions of the equation are points that lie on the graph and all the points that lie on the graph are solutions of the equation.
How is an inequality and a two step equation the same?
An inequality and a two-step equation are similar in that both involve algebraic expressions and require solving for a variable. Each represents a relationship between quantities, with equations showing equality and inequalities showing a range of possible values (greater than, less than, etc.). Both require similar techniques, such as isolating the variable, but while equations yield a specific solution, inequalities provide a set of possible solutions. Ultimately, both are essential tools in algebra for modeling and solving problems.
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