You can put this solution on YOUR website! Find the coordinates of any points of intersection of the graphs of 2x - y = 1 and y = 5 - 5x - 3x^2
:
Arrange the 1st equation for substitution for y
2x - y = 1
-y = -2x + 1
y = 2x - 1; multiplied by -1
:
y = 5 - 5x - 3x^2
:
replace y with (2x-1)
2x - 1 = 5 - 5x - 3x^2
:
Combine like terms on the left side
3x^2 + 2x + 5x - 1 - 5 = 0
;
A quadratic equation
3x^2 + 7x - 6 = 0
:
Factors to
(3x - 2)(x + 3) = 0
Two solutions
x = -3
and
3x = 2
x =
:
Find y using the 1st equation when x=-3
y = 2(-3) - 1
y = -7
Find y when x = 2/3
y = 2(2/3) - 1
y = (4/3) - 1
y =
:
Points of intersection: -3,-7, and ,
:
Graphically
