Question

X+2Y=5 and 2X+3Y=8. Find the Mean of X and Y.

Hint:

To find the mean of X and Y, solve the system of equations to find the values of X and Y, then calculate their average.

Answer 1

Step 1: Solve the system of equations.
We are given two linear equations: \[ X + 2Y = 5 \quad \text{(Equation 1)} \] \[ 2X + 3Y = 8 \quad \text{(Equation 2)} \] We will solve these equations to find the values of X and Y.
Step 2: Eliminate one variable.
We can eliminate X by multiplying Equation 1 by 2: \[ 2(X + 2Y) = 2(5) \] \[ 2X + 4Y = 10 \quad \text{(Equation 3)} \] Now subtract Equation 2 from Equation 3: \[ (2X + 4Y) - (2X + 3Y) = 10 - 8 \] \[ Y = 2 \]
Step 3: Substitute the value of Y into one equation.
Substitute \(Y = 2\) into Equation 1: \[ X + 2(2) = 5 \] \[ X + 4 = 5 \] \[ X = 1 \]
Step 4: Calculate the mean of X and Y.
The mean of X and Y is: \[ \text{Mean} = \frac{X + Y}{2} = \frac{1 + 2}{2} = \frac{3}{2} = 1.5 \]