Algebra 1

Answers may vary Two solutions: $y=2x^2+10x+9$ and $y=x$ ($x= -1.5, -3$) One solution: $y=x^2+2x+1$ and $y=x+.75$ ($x=-.5$) No solutions: $y=x^2+x+3$ and $y=x$
Two solutions: $y=2x^2+10x+9$ and $y=x$ $2x^2+10x+9=x$ $2x^2+10x-x+9=x-x$ $2x^2+9x+9=0$ $x=(-b±\sqrt {b^2-4ac})/2a$ $x=(-9±\sqrt {9^2-4*2*9})/2*2$ $x=(-9±\sqrt {81-72})/4$ $x=(-9±\sqrt {9})/4$ $x=(-9±3)/4$ $x=(-9+3)/4$ $x=-6/4 = -1.5$ $x=(-9-3)/4$ $x=-12/4 =-3$ One solution: $y=x^2+2x+1$ and $y=x+.75$ $x^2+2x+1=x+.75$ $x^2+2x+1-x-.75=x+.75-x-.75$ $x^2+x+.25=0$ $x=(-b±\sqrt {b^2-4ac})/2a$ $x=(-1±\sqrt {1^2-4*1*.25})/2*1$ $x=(-1±\sqrt {1-1})/2$ $x=(-1±\sqrt {0})/2$ $x=(-1±0)/2$ $x=-1/2$ No solutions: $y=x^2+x+3$ and $y=x$ $x^2+x+3=x$ $x^2+x+3-x=x-x$ $x^2+3 =0$ $x=(-b±\sqrt {b^2-4ac})/2a$ $x=(-0±\sqrt {0^2-4*1*3})/2*1$ $x=(±\sqrt {0-12})/2$ $x=(±\sqrt {-12})/2$ We can't have the square root of a negative number, so there are no solutions.