Solving Simultaneous Equations using Substitution Method
In this article, we will solve the following system of linear equations using the substitution method:
Equations:
- 1/5x + 1/6y = 12
- 1/3x - 3/7y = 8
Step-by-Step Solution:
Step 1: Solve one of the equations for one variable.
Let's solve the first equation for x:
1/5x + 1/6y = 12
Multiply both sides by 5 to eliminate the fraction:
x + 5/6y = 60
Now, solve for x:
x = 60 - 5/6y
Step 2: Substitute the expression into the other equation.
Substitute the expression for x into the second equation:
1/3(60 - 5/6y) - 3/7y = 8
Step 3: Simplify and solve for y.
Expand and simplify the equation:
20 - 5/6y - 3/7y = 8
Combine like terms:
-25/42y = -12
Multiply both sides by -42 to eliminate the fraction:
25y = 504
Divide by 25:
y = 504/25 y = 20.16
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Substitute y = 20.16 into the expression for x:
x = 60 - 5/6(20.16)
x = 60 - 16.80 x = 43.20
Step 5: Write the final solution.
x ≈ 43.20 y ≈ 20.16
Therefore, the solution to the system of linear equations is x ≈ 43.20 and y ≈ 20.16.
