Answer:
x = 1, y = 5
x = 5, y = 13
Step-by-step explanation:
y = x² − 4x + 8 .......(1)
y = 2x + 3 .......(2)
Substitute the value of y in equation 2 into equation 1
y = x² − 4x + 8
y = 2x + 3
x² − 4x + 8 = 2x + 3
Rearrange
x² − 4x − 2x + 8 − 3 = 0
x² − 6x + 5 = 0
Solve by factorization
Find the product you x² and 5. The result is 5x²
Find the factors of 5x² such that their sum will result in −6x. The factors are −x and −5x.
Replace −6x in the equation above with −x and −5x. This is illustrated below:
x² − x − 5x + 5 = 0
x(x − 1) − 5(x − 1) = 0
(x − 1)(x − 5) = 0
x − 1 = 0 or x − 5 = 0
x = 1 or x = 5
Substitute the value of x into equation 2 to obtain the value of y.
y = 2x + 3
x = 1
y = 2(1) + 3
y = 2 + 3
y = 5
x = 5
y = 2x + 3
y = 2(5) + 3
y = 10 + 3
y = 13
SUMMARY:
x = 1, y = 5
x = 5, y = 13
