Question

Solve the system of equations.

y=x²-5
y= -2x+3
A. (-2, 7) and (4,-5)
OB. (-4, 11) and (2, -1)
OC. (2,-1) and (4,-5)
OD. (-4, 11) and (-2,7)

Answer 1

`y= x^2 -5~~~~~~...(i)\\\\y = -2x +3~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~~~~x^2 -5 = -2x+3\\\\\implies x^2 -5 +2x -3 = 0\\\\\implies x^2 +2x -8 = 0 \\\\\implies x^2 +4x -2x -8 = 0\\\\\implies x(x+4) -2(x+4) = 0\\\\\implies ( x+4)(x-2) = 0\\ \\\implies x = -4,~ x = 2\\\\\text{Substitute x = 2 in eq (ii)}:\\\\y = -2(2) +3 = -4 +3 = -1\\\\\text{Substitute}~ x = -4 ~\text{in eq (ii)}:\\\\y = -2(-4) +3 = 8 +3 = 11\\\\\text{So,} ~(x, y)=\{(2,-1), (-4,11) \}\\\\\text{Hence the answer is option B.}`