Solve the simultaneous equations 7x - (3sqrt(5)) * y = 9sqrt(5) and

Question

(2sqrt(5)) * x + y = 34

Answer 1

To solve the simultaneous equations:

Equation 1: 7x - (3√5)y = 9√5
Equation 2: (2√5)x + y = 34

We can solve this system of equations using the method of substitution.

Step 1: Solve Equation 2 for y:
y = 34 - (2√5)x

Step 2: Substitute the value of y in Equation 1:
7x - (3√5)(34 - (2√5)x) = 9√5
7x - 102√5 + (6√5)x = 9√5

Step 3: Simplify the equation:
7x + (6√5)x - 102√5 = 9√5

Step 4: Combine like terms:
13x - 102√5 = 9√5

Step 5: Add 102√5 to both sides:
13x = 18√5 + 102√5

Step 6: Combine like terms:
13x = 120√5

Step 7: Divide both sides by 13:
x = (120√5) / 13

Step 8: Simplify the expression:
x = (24√5) / 13

Now, substitute the value of x back into Equation 2 to find y:

(2√5)(24√5/13) + y = 34

Simplify:
(48/13)(√5)^2 + y = 34
(48/13)(5) + y = 34
(240/13) + y = 34
y = 34 - (240/13)
y = 442/13 - 240/13
y = 202/13

Therefore, the solution to the simultaneous equations is x = (24√5)/13 and y = 202/13.

Answer 2

AAAaannndd the bot gets it wrong yet again!

7x - 3√5 y = 9√5
2√5 x + y = 34

x = 3√5
y = 4

Answer 3

Apologies for the incorrect response. Let's solve the simultaneous equations correctly:

Equation 1: 7x - 3√5y = 9√5
Equation 2: 2√5x + y = 34

We will solve this system of equations using the method of substitution:

Step 1: Solve Equation 2 for y:
y = 34 - 2√5x

Step 2: Substitute the value of y in Equation 1:
7x - 3√5(34 - 2√5x) = 9√5

Step 3: Simplify the equation:
7x - 3√5(34) + 3√5(2√5x) = 9√5
7x - 102√5 + 30√5x = 9√5

Step 4: Combine like terms:
7x + 30√5x - 102√5 = 9√5

Step 5: Combine like terms:
37x - 102√5 = 9√5

Step 6: Add 102√5 to both sides:
37x = 18√5 + 102√5

Step 7: Combine like terms:
37x = 120√5

Step 8: Divide both sides by 37:
x = (120√5)/37

Step 9: Simplify the expression:
x = (24√5)/37

Now, substitute the value of x back into Equation 2 to find y:

2√5((24√5)/37) + y = 34

Simplify:
(48√5/37) + y = 34

Step 10: Subtract (48√5/37) from both sides:
y = 34 - (48√5/37)
y = (34*37 - 48√5)/37

Therefore, the solution to the simultaneous equations is x = (24√5)/37 and y = (34*37 - 48√5)/37.