Answer:
(- 5, 0), (3, 4)
Step-by-step explanation:
Given the 2 equations
2y - x = 5 → (1)
x² + y² - 25 = 0 → (2)
Rearrange (1) expressing x in terms of y
x = 2y - 5 → (3)
Substitute x = 2y - 5 into (2)
(2y - 5)² + y² - 25 = 0 ← expand parenthesis and simplify
4y² - 20y + 25 + y² - 25 = 0
5y² - 20y = 0 ← factor out 5y from each term
5y(y - 4) = 0
Equate each factor to zero and solve for y
5y = 0 ⇒ y = 0
y - 4 = 0 ⇒ y = 4
Substitute these values into (3) for corresponding values of x
y = 0 : x = 0 - 5 = - 5 ⇒ (- 5, 0)
y = 4 : x = 8 - 5 = 3 ⇒ (3, 4)
Answer:
y=0 or 4, x=-5 or 3
Step-by-step explanation:
First make one unknown in the first equation the subject of the formula.
2y-x=5 will become:x=2y-5
Then in the second equation, wherever there is x we substitute it with 2y-5
(2y-5)²+y²-25=0 (2y-5)(2y-5)+y²-25=0
opening the brackets gives: 4y²-10y-10y+25+y²-25=0
5y²-20y=0
Factorizing the equation we get the following:
y(5y-20)=0
y=0 or
5y-20=0
5y=20
y=4
Thus y=0 or 4
Substitute 0 and 4 for y in any of the equations provided.
Picking the first equation and starting with y=0
2(0)-x=5
x=-5
Using y=4
2(4)-x=5
x=3
