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.
Solve the simultaneous equations 7x - (3sqrt(5)) * y = 9sqrt(5) and
(2sqrt(5)) * x + y = 34
3 answers
AAAaannndd the bot gets it wrong yet again!
7x - 3√5 y = 9√5
2√5 x + y = 34
x = 3√5
y = 4
7x - 3√5 y = 9√5
2√5 x + y = 34
x = 3√5
y = 4
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.
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.