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We must use the substitution method for this question because the first equation is a quadratic. Take the more simple equation (the second one), and use that to substitute the value for y in to the first ...

Using the product rule (u'v+v'u, where u and v are the chosen substitutes) to find the first derivative will be dy/dx=x'=2xe^(-2x)+x^(2)e^(-2x)(-2)=2xe^(-2x)(x-x^2). This will give the d...

To solve these simultaneous equations there are two different methods that could be used. The first one to try in this case is to start with rearranging one of the equations to get a value of y by itself....

equation 1: 2y + x = 8equation 2: 4 + 4y = 8xSolve by substitution;simplify equation 12y + x = 8 x = 8 - 2ysubstitute into equation 2 4 + 4y = 8(8 - 2y)4 + 4...

Multiply out the right hand side so equation becomes 3x+10=20x-50Move x's to one side and numbers to other so 17x = 60x= 60/17