Answer:
Explanation:
The system of equations is expressed as
x + y = 8 - - - - - - - - - - - - - -1
x² + y² = 34 - - - - - - - - - - - -2
From equation 1, we would make x to stand alone by subtracting y from the left hand side and the right hand side of the equation. It becomes
x + y - y = 8 - y
x = 8 - y
Substituting x = 8 - y into equation 2, it becomes
(8 - y)² + y² = 34
(8 - y)(8 - y) + y² = 34
64 - 8y - 8y + y² + y² = 34
2y² - 16y + 64 - 34 = 0
2y²- 16y + 30 = 0
Dividing through by 2, it becomes
y² - 8y + 15 = 0
y² - 5y - 3y + 15 = 0
y(y - 5) - 3(y - 5) = 0
y - 5 = 0 or y - 3 = 0
y = 5 or y = 3
Recall, x = 8 - y
x = 8 - 5. or x = 8 - 3
x = 3 or x = 5