Let's warm up by solving the following
equations:
i) x2 - 5x + 6 = y, y = x - 1
ii) 2x2 - 3x - 5 = y, (2x + 2)/4 = y
iii) 2x + y = 4, 2x2 + 5x - 3 = y
iv) a2 - 3a + 5 = b, a + b = 5
Hint! y = x2 - 5x + 6 and y = x - 1 can be
written as x2 - 5x + 6 = x - 1 since they are both equal to y
and as such they can be equated together (think of substitution
method). This idea is very useful when solving such equations,
since graphing calculator can not allow you to type two
equations in the form of that in (i) to (iii) above.
Solutions
i) x = 4.41421 and y = 3.541421
or x = 1.58579 and y = 0. 585786
ii) x = 4.63314 and y = 2.56657
or x= -1.13314 and -0.31657
iii) x = 0.811738 and y = 2.37652
x = -4.31174 and 12.6235
iv) a = 2 and b = 3
a = 0 and b = 5
Solving two quadratic equations.
The solution of these two will also be
given by the intersection of the two curves. Try and solve the
following simultaneous equations.
i) x2 - 5x + 6 = y , 2x2 + 3x - 4 = y
ii) 4x2 - x + 3 = y , y = x2 - 5x + 10
iii) a2 + 5b + 6 = b, b = 2a2 - 3a - 7
iv) a2 -3b + 5 = 3a, 5b - 3a2 + 8 = 4