Given
Find
- x and y that are solutions to these equations
Solution
It can work well to equate the expressions for y, then put the quadratic into standard form and solve in any of the ways you've been taught.
... x² -2x = 2x -3
... x² -4x +3 = 0
... (x -1)(x -3) = 0 . . . . . . . . factor. Choose factors of 3 that sum to -4: {-1, -3}.
By the zero-product rule, the product can only be zero if one or more factors is zero.
First factor:
... x -1 = 0
... x = 1 . . . . . . add 1
Second factor:
... x -3 = 0
... x = 3 . . . . . . add 3
The solutions for x are 1 and 3. The corresponding solutions for y are ...
... 2x -3 = 2·1 -3 = -1
... 2x -3 = 2·3 -3 = 3
Soutions to these equations are
- (x, y) = (1, -1)
- (x, y) = (3, 3)