Use the substitution method to solve the system of equations. 4x-8y=0 , x^2 + y^2 = 25.?

Question

Use the substitution method to solve the system of equations. 4x-8y=0 , x^2 + y^2 = 25.? 
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Use the substitution method to solve the system of equations.
4x-8y=0
x^2 + y^2 = 25

Step 1: Solve the equation 4x-8y=0 for x. Show work.
x=__________.


Step 2: Substitute the expression you found for x in step 1 into the equation x^2+y^2=25. Then solve for y. Show work.
(_ _ _ _ _) +y^2 = 25


Step 3: Once you know the values of y, substitute them back into the first equation to find the corresponding values of x. Show work.

Step 4: Write your solutions as ordered pairs.
(______, ______) and (______, ______)

Answer 1

4x - 8y = 0

x² + y² = 25

 

Step 1.

4x - 8y = 0

4x = 8y

x = 2y

 

Step 2.

x² + y² = 25

(2y)²  + y² = 25

4y² + y² = 25

5y² = 25

y² = 5

√y² = √5

y = ±√5

 

Step 3.

x = 2y

When y = +√5:

x = 2√5

When y = -√5:
x = -2√5

 

Step 4.

(2√5,√5) and (-2√5,-√5):

Step 5 - Check you answers!

4x - 8y = 0
x² + y² = 25

 

For (-2√5,-√5):

4(-2√5) - 8(-√5) = 0

-8√5 + 8√5 = 0

0 = 0   check!

(-2√5)² + (-√5)² = 25

4*5 + 5 = 25

25=25  check!

 

For (2√5,√5):

4(2√5) - 8(√5) = 0
8√5 - 8√5 = 0
0 = 0 check!
(2√5)² + (√5)² = 25
4*5 + 5 = 25
25=25 check!