SOLUTION: What is the x, y values for the eqautions y=-2x+7, and y=x^2-4x, I need to find the x, y values then plott onto a graph. Donetta McCormick

Algebra ->  Graphs -> SOLUTION: What is the x, y values for the eqautions y=-2x+7, and y=x^2-4x, I need to find the x, y values then plott onto a graph. Donetta McCormick      Log On


   

Question 357156: What is the x, y values for the eqautions y=-2x+7, and y=x^2-4x, I need to find the x, y values then plott onto a graph.
Donetta McCormick
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=-2x%2B7 Start with the first equation.


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


x%5E2-4x%2B2x-7=0 Get every term to the left side.


x%5E2-2x-7=0 Combine like terms.


Notice that the quadratic x%5E2-2x-7 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-2, and C=-7


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-7%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=-7


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-7%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%28-7%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--28+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-7%29 to get -28


x+=+%282+%2B-+sqrt%28+4%2B28+%29%29%2F%282%281%29%29 Rewrite sqrt%284--28%29 as sqrt%284%2B28%29


x+=+%282+%2B-+sqrt%28+32+%29%29%2F%282%281%29%29 Add 4 to 28 to get 32


x+=+%282+%2B-+sqrt%28+32+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+4%2Asqrt%282%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%29%2F%282%29+%2B-+%284%2Asqrt%282%29%29%2F%282%29 Break up the fraction.


x+=+1+%2B-+2%2Asqrt%282%29 Reduce.


x+=+1%2B2%2Asqrt%282%29 or x+=+1-2%2Asqrt%282%29 Break up the expression.


So the solutions are x+=+1%2B2%2Asqrt%282%29 or x+=+1-2%2Asqrt%282%29


Now let's find the corresponding y values.


Let's find the value of y when x+=+1%2B2%2Asqrt%282%29


y=-2x%2B7 Start with the first equation.


y=-2%281%2B2%2Asqrt%282%29%29%2B7 Plug in x+=+1%2B2%2Asqrt%282%29


y=-2-4%2Asqrt%282%29%2B7 Distribute.


y=5-4%2Asqrt%282%29 Combine like terms.


So when x+=+1%2B2%2Asqrt%282%29, y=5-4%2Asqrt%282%29 which gives us the ordered pair


Now let's find the value of y when x+=+1-2%2Asqrt%282%29


y=-2x%2B7 Start with the first equation.


y=-2%281-2%2Asqrt%282%29%29%2B7 Plug in x+=+1-2%2Asqrt%282%29


y=-2%2B4%2Asqrt%282%29%2B7 Distribute.


y=5%2B4%2Asqrt%282%29 Combine like terms.


So when x+=+1-2%2Asqrt%282%29, y=5%2B4%2Asqrt%282%29 which gives us the ordered pair