SOLUTION: Solve the simultaneous equations y=x^2-5x+6 and x+y=2. Show that the line x+y=2 is a tangent to the curve y=x^2-5x+6 at one of the points where the curve intersects the axes

Algebra ->  Graphs -> SOLUTION: Solve the simultaneous equations y=x^2-5x+6 and x+y=2. Show that the line x+y=2 is a tangent to the curve y=x^2-5x+6 at one of the points where the curve intersects the axes      Log On


   

Question 919360: Solve the simultaneous equations y=x^2-5x+6 and x+y=2. Show that the line x+y=2 is a tangent to the curve y=x^2-5x+6 at one of the points where the curve intersects the axes
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2-5x%2B6 .......1
x%2By=2.......2
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x%2By=2.......2.....plug in y from 1
x%2Bx%5E2-5x%2B6=2 ...........solve for x
x%5E2-4x%2B6-2=0
x%5E2-4x%2B4=0
x%5E2-2x-2x%2B4=0
%28x%5E2-2x%29-%282x-4%29=0
x%28x-2%29-2%28x-2%29=0
%28x-2%29%28x-2%29=0 => double solution x=2
go to
y=x%5E2-5x%2B6 .......plug in 2 for x and solve for y
y=2%5E2-5%2A2%2B6
y=4-10%2B6
y=10-10
y=0

so,these lines intercept at (2,0) and a tangent line to the curve y=x%5E2-5x%2B6 is at x=2,the point where the curve intersects the x-axis

+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+-x%2B2%2C+x%5E2-5x%2B6%29+