What is the solution of the linear-quadratic system of equations? { y = x 2 + 5 x − 3 y − x = 2

Try substituting those values, and you will see they do not fit either equation.

looking at the 2nd equation, y = x+2, so

x+2 = x^2+5x-3

x^2 + 4x - 5 = 0

(x+5)(x-1) = 0

x = -5 or 1

so, y = -3 or 3

the solutions are thus (-5,-3)(1,3)

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Answer-

(-5,-3)(1,3)

How I got my answer-

×+2=×^2+5×-3

×^2+4×-5=0

(×+5)(×-1)=0

×= -5 or 1

and y=3 or 3