Question 1197265
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Reduce two starting equations to one single equation for x, eliminating y

    x^2 - 7x + 15 = 2x - 5


Write it in the standard form

    x^2 - 9x + 20 = 0


Factor left side

    (x-4)*(x-5) = 0


The roots are 4 and 5.


For each root calculate y


    {{{y[1]}}} = {{{2*x[1]-5}}} = 2*4 - 5 = 3;

    {{{y[2]}}} = {{{2*x[2]-5}}} = 2*5 - 5 = 5.


<U>ANSWER</U>.  There are 2 solutions:  (1)  (x,y) = (4,3)  and  (2)  (x,y) = (5,5).
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Solved, with full explanations.