Final answer:
To solve the simultaneous equations 4x - 0.5y = 12.5 and 3x + 0.8y = 8.2, we can use the method of elimination. Multiply the equations to eliminate the variable y, and then solve for x and y. The solution is x = 3 and y = -1.
Step-by-step explanation:
To solve the simultaneous equations:
Equation 1: 4x - 0.5y = 12.5
Equation 2: 3x + 0.8y = 8.2
We can use the method of substitution or elimination to solve these equations.
Using the method of elimination, we can multiply Equation 1 by 3 and Equation 2 by 4 to eliminate the variable y:
Equation 1: 12x - 1.5y = 37.5
Equation 2: 12x + 3.2y = 32.8
Now subtract Equation 1 from Equation 2:
12x + 3.2y - (12x - 1.5y) = 32.8 - 37.5
4.7y = -4.7
y = -4.7/4.7
y = -1
Substitute the value of y back into either equation to find x:
Equation 1: 4x - 0.5(-1) = 12.5
4x + 0.5 = 12.5
4x = 12.5 - 0.5
4x = 12
x = 12/4
x = 3
Therefore, the solution to the simultaneous equations is x = 3 and y = -1.