Question

Solve the following system of equations algebraically:
y = x2 + 5x - 17
y=x-5

Answer 1

`\left \{ {\big{y = x^2 + 5x - 17} \atop \big{y=x-5\qquad \quad\ }} \right. \\\\ \left \{ {\big{x-5 = x^2 + 5x - 17} \atop \big{y=x-5\qquad \qquad\ \ }} \right. \\\\ \left \{ {\big{ x^2 + 6x-2x - 12=0} \atop \big{y=x-5\qquad \qquad\ }} \right. \\\\ \left \{ {\big{ x^2 - 2x +6x- 12=0} \atop \big{y=x-5\qquad \qquad\ \quad }} \right. \\\\ \left \{ {\big{ x(x - 2) +6(x- 2)=0} \atop \big{y=x-5\qquad \qquad\ \quad\ }} \right.`


`\left \{ {\big{ (x- 2)(x +6)=0} \atop \big{y=x-5\qquad \quad }} \right. \\\\ \left \{ {\big{ x- 2=0} \atop \big{y=x-5 }} \right. \ \quad \quad \ or\ \ \quad \ \left \{ {\big{ x +6=0} \atop \big{y=x-5 }} \right.\\\\ \left \{ {\big{ x=2\ \ \ \ } \atop \big{y=2-5 }} \right. \ \quad \quad \ or\ \ \quad \ \left \{ {\big{ x =-6\ \ \ } \atop \big{y=-6-5 }} \right. \\\\ \left \{ {\big{ x=2\ \ \ \ } \atop \big{y=-3 }} \right. \ \quad \quad \ or\ \ \quad \ \left \{ {\big{ x =-6\ \ \ } \atop \big{y=-11 }} \right.`