Answer:
x = 1, y = −1
x = 5/2, y = 1/2
Explanation:
From the question given above, the following data were obtained:
y = 2x² − 6x + 3 ........ (1)
y = x − 2 ...... (2)
We can obtain the solutions to the equation as follow:
y = 2x² − 6x + 3 ........ (1)
y = x − 2 ...... (2)
Substitute the value of y in equation 2 into equation 1
y = 2x² − 6x + 3
y = x − 2
2x² − 6x + 3 = x − 2
Rearrange
2x² − 6x − x + 3 + 2 = 0
2x² − 7x + 5 = 0
Solve by factorization
Obtain the product of 2x² and 5. The result is 10x².
Find two factors of 10x² such that their sum will result to −7x.
The factors are −2x and −5x.
Replace −7x in the equation above with −2x and −5x as shown below:
2x² − 2x − 5x + 5 = 0
2x(x − 1) − 5(x − 1) = 0
(x − 1)(2x − 5) = 0
x − 1 = 0 or 2x − 5 = 0
x = 1 or 2x = 5
x = 1 or x = 5/2
Substitute the value of x into equation 2 to obtain y
y = x − 2
x = 1
y = 1 − 2
y = −1
x = 5/2
y = x − 2
y = 5/2 − 2
y = (5 − 4)/2
y = 1/2
SUMMARY:
x = 1, y = −1
x = 5/2, y = 1/2