Final answer:
To solve the simultaneous equations, manipulate one to match the coefficient of y in the other, subtract, simplify, isolate y, substitute back to find x, and then y. Finally, check the solution in the original equations.
Step-by-step explanation:
To solve the given simultaneous equations, we need to manipulate the equations algebraically to find the values of x and y. The given equations are:
- 32x + 22y = 33 (Equation 1)
- 44x - 24y = 6 (Equation 2)
Let's multiply Equation 1 by a number that will make the coefficients of y in both equations match in absolute value. In this instance, multiplying by 2 seems suitable:
- 64x + 44y = 66 (Equation 3)
Now subtract Equation 2 from Equation 3:
- (64x + 44y) - (44x - 24y) = 66 - 6
- 20x + 68y = 60
Next, divide the entire equation by 4 to simplify:
- 5x + 17y = 15 (Equation 4)
We can solve for y by isolating it in Equation 4:
- 17y = 15 - 5x
- y = (15 - 5x) / 17
Let's substitute this y back into Equation 1 or 2 to find x. After finding x, we can substitute it back into Equation 4 to find y. Remember to check your solutions in both original equations to confirm their correctness.