#"to graph "x+y=5" find the intercepts"#
#• " let x = 0, in the equation for y-intercept"#
#• " let y = 0, in the equation for x-intercept"#
#x=0to 0+y=5rArry=5larrcolor(red)"y-intercept"#
#y=0tox+0=5rArrx=5larrcolor(red)"x-intercept"#
#"plot "(0,5)" and "(5,0)#
#"and draw a straight line through them"#
#"to graph "y=4/x#
#"x cannot equal zero as this would make y undefined"#
#x=0" is a vertical asymptote"#
#y!=0" so there are no x-intercepts"#
#"choose some values for x and calculate y"#
#x=1toy=4/1=4rArr(1,4)" is a point"#
#x=2toy=4/2=2rArr(2,2)" is a point"#
#x=4toy=4/4=1rArr(4,1)" is a point"#
#"draw a smooth curve through these points for graph"#
#color(blue)"find the intersection using algebraic method"#
#"substitute "y=4/x" into "x+y=5#
#rArrx+4/x=5#
#"multiply through by x and equate to zero"#
#rArrx^2-5x+4=0larrcolor(blue)"factorise"#
#rArr(x-1)(x-4)=0#
#x-1=0rArrx=1#
#x-4=0rArrx=4#
#"find corresponding y coordinates"#
#x=1toy=4" and "x=4toy=1#
#rArr"points of intersection are "(1,4)" and "(4,1)#
graph{(y+x-5)(y-4/x)((x-1)^2+(y-4)^2-0.04)((x-4)^2+(y-1)^2-0.04)=0 [-10, 10, -5, 5]}
