Help me please!!

Question

Solve each system of equations by using substitution

{x-2y=0 {4y=x

{x²+y²=125 {x²-y²=60

Please show your work

Answer 1

In the first set of equations x-2y=0 and x² +y² =125 using the first equation x² -4y² =0 or x² =4y² substitute this into the second equation to get 4y² + y² =125 then 5y² =125 and y² =25 giving y =±5. Going back to second equation x² 25 = 125 and x² = 100 giving x=± 10.

In the second set of equations 4y=x and x² -y²= 60 again square the first equation to get 16y²=x² and substitute this into the second equation to get 16y² -y² = 60 giving 15y²= 60 or y²= 4 and hence y=±2. Substitute this back in to the second equation to get x²- 4 = 60 and x² =64 so x= ±8

Answer 2

First set of equations

x-2y=0

x²+y²=125

x = 2y <--- Rearranging the first equation

x²+y²=125

(2y)² +y²=125 Substituting the first equation into the second equation thus eliminating x.

4y² + y² = 125

5y² = 125

y² = 25

y = +/- 5

Now that we know that y² = 25, substitute for it in the second original equation.

x²+y²=125

x² + 25 =125

x² = 100

x = +/- 10

Therefore, altogether

x = +/- 10 and y = +/- 5

Second Set of Equations

4y=x

x²-y²=60

Substitute the first equation into the second thus eliminating x.

(4y)² - y²=60

16y² - y² = 60

15y² = 60

y² = 4

y = +/- 2

Substitute for y² = 4 in the second original equation.

x² - 4 = 60

x² = 64

x = +/- 8

Altogether, we have

x = +/- 8

y = +/- 2