Solving the System of Linear Equations using Elimination Method
Given Equations:
$\frac{1}{2}x + \frac{1}{3}y = 2$
$\frac{1}{3}x + \frac{1}{2}y = \frac{13}{6}$
Goal: Find the values of x and y using the Elimination Method.
Step 1: Make the coefficients of y's opposites
Multiply equation (1) by 2 and equation (2) by 3 to make the coefficients of y's opposites:
Equation (1): $x + \frac{2}{3}y = 4$
Equation (2): $x + \frac{3}{2}y = \frac{13}{2}$
Step 2: Eliminate y
Subtract equation (1) from equation (2) to eliminate y:
$\frac{1}{6}y = \frac{5}{2}$
Step 3: Solve for y
Multiply both sides by 6 to get:
$y = 15$
Step 4: Substitute y into one of the original equations
Substitute y = 15 into equation (1):
$x + 10 = 4$
Step 5: Solve for x
Subtract 10 from both sides to get:
$x = -6$
Solution:
x = -6 y = 15
Check: Verify that the solution satisfies both original equations.
