SOLUTION: Hello I have a problem that is nonlinear and cramer's rule or Gaussian elimination can't be used for. I'm trying to use substitution and factoring for this one but I'm coming u

Algebra ->  Systems-of-equations -> SOLUTION: Hello I have a problem that is nonlinear and cramer's rule or Gaussian elimination can't be used for. I'm trying to use substitution and factoring for this one but I'm coming u      Log On


   

Question 252265: Hello
I have a problem that is nonlinear and cramer's rule or Gaussian elimination can't be used for. I'm trying to use substitution and factoring for this one but I'm coming up with the right thing... And I know its something that I'm missing I just can't see it.... it seems like the simplier the problem, I make mistakes.

Could you please assist me with solving this problem ..
Thanks
y=x^2-4x+7
y=x+1


Found 2 solutions by jim_thompson5910, actuary:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2-4x%2B7 Start with the first equation.


x%2B1=x%5E2-4x%2B7 Plug in y=x%2B1


0=x%5E2-4x%2B7-x-1 Get everything to one side.


0=x%5E2-5x%2B6 Combine like terms.


0=%28x-3%29%28x-2%29 Factor the right side.


x-3=0 or x-2=0 Use the zero product property.


x=3 or x=2 Solve for 'x' in each equation.


Now for each 'x', plug them into y=x%2B1 to find the corresponding 'y' values.


So when x=3, then y=3%2B1=4 which gives the first ordered pair (3,4)


and when x=2, then y=2%2B1=3 which gives the second ordered pair (2,3)



Answer by actuary(112) About Me  (Show Source):
You can put this solution on YOUR website!
Since x+1 = y AND y=x^2-4x+7, x+1 = x^2-4x+7
This equation can be rewritten as 0 = x^2-5x+6.
This equation can be factored into linear expressions so x^2-5x+6=(x-3)*(x-2)=0
So x=3 and x = 2.
Next each of values for x can be substituted in either equation to determine the values of y.
Using the equation y = x +1.
When x = 2, y = 2+1 = 3
When x = 3, y = 3+1 = 4.
So, there are two solutions to the system of equations.
You may want to graph both equation to "see" the points of intersection of the two graphs.