Question

Solve this system of equations to find x and y, please, and explain how you did it:

Answer 1

Answer:

Step-by-step 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