solve simultaneous equation
1/2x+2y=16
2x +1/2y=19
To solve the simultaneous equations:
Equation 1: (1/2)x + 2y = 16
Equation 2: 2x + (1/2)y = 19
Let's solve the system using the method of elimination:
Step 1: Multiply Equation 1 by 4 and Equation 2 by 2 to get rid of the fractions.
Equation 1 becomes: 2x + 8y = 64
Equation 2 becomes: 4x + y = 38
Now we have two new equations:
Equation 3: 2x + 8y = 64
Equation 4: 4x + y = 38
Step 2: Multiply Equation 3 by 2 and subtract Equation 4 from it to eliminate x.
(2 * Equation 3) - Equation 4:
(2 * (2x + 8y)) - (4x + y)
4x + 16y - 4x - y = 128 - 38
15y = 90
y = 90 / 15
y = 6
Step 3: Substitute the value of y (6) back into one of the original equations to solve for x.
Using Equation 1:
(1/2)x + 2(6) = 16
(1/2)x + 12 = 16
(1/2)x = 16 - 12
(1/2)x = 4
x = (4 * 2) / 1
x = 8
Therefore, the solution to the simultaneous equations is x = 8 and y = 6.