Final answer:
To solve the pair of simultaneous equations, 2x+5y=6 1/2 and 5x-2y=9, we can use the method of substitution. Solving for y and x, we find that y = 9/29 and x = 37/29.
Step-by-step explanation:
To solve the pair of simultaneous equations 2x+5y=6½ and 5x-2y=9, we can use the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for x:
5x = 9 + 2y ⟶ x = (9 + 2y) / 5
Step 2: Substitute the expression for x from step 1 into the other equation:
2[(9 + 2y) / 5] + 5y = 6½
Simplify and solve for y:
18 + 4y + 25y = 27
29y = 9
y = 9/29
Step 3: Substitute the value of y back into one of the original equations to solve for x:
2x + 5(9/29) = 6½
Simplify and solve for x:
2x = 6½ - 45/29
2x = 119/29 - 45/29
2x = 74/29
x = 74/58
Therefore, the solution to the pair of simultaneous equations is x = 37/29 and y = 9/29.