determine which ordered pair is a solution of the system

The quickest way here is just to substitute each set of coordinates into both equations to see which set makes both equations true.

 

Alternatively:

 

Multiply first equation by 5:           -35x + 10y^2 = -50      (1)

Multiply second equation by 7:     -35x - 14y  = -154        (2)

 

Subtract (2) from (1) term by term   0 + 10y^2 + 14y = 104  or, dividing by 2:  5y^2 + 7y = 52

Write this as:  5y^2 + 7y - 52 = 0  

Solving this we get y = -4 and y = 13/5

 

Looking at the [possible solution sets provided we can see that it is y = -4 that we want.

 

Plug this into -5x - 2y = -22 to get -5x + 8 = -22  or 5x = 30  so x = 6.

 

Solution is (6, -4)

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