Solving Simultaneous Equations: 3x - 2y + 3 = 0 and 4x + 3y - 47 = 0 using Substitution Method
In this article, we will learn how to solve a system of linear equations using the substitution method. The given equations are:
Equation 1: 3x - 2y + 3 = 0 Equation 2: 4x + 3y - 47 = 0
Step 1: Solve one of the equations for one variable
We will solve Equation 1 for y:
3x - 2y + 3 = 0
Subtract 3 from both sides:
3x - 2y = -3
Divide both sides by -2:
y = (3x + 3)/2
Step 2: Substitute the expression from Step 1 into the other equation
Substitute the expression for y into Equation 2:
4x + 3((3x + 3)/2) - 47 = 0
Step 3: Simplify the equation
Multiply the term inside the parenthesis by 3:
4x + (9x + 9)/2 - 47 = 0
Multiply both sides by 2 to eliminate the fraction:
8x + 9x + 9 - 94 = 0
Combine like terms:
17x - 85 = 0
Step 4: Solve for x
Add 85 to both sides:
17x = 85
Divide both sides by 17:
x = 85/17 x = 5
Step 5: Find the value of y
Substitute the value of x into the expression for y:
y = (3(5) + 3)/2 y = (15 + 3)/2 y = 18/2 y = 9
Solution
The solution to the system of linear equations is x = 5 and y = 9.
Verification
Substitute the values of x and y into both equations to verify the solution:
Equation 1: 3(5) - 2(9) + 3 = 15 - 18 + 3 = 0 Equation 2: 4(5) + 3(9) - 47 = 20 + 27 - 47 = 0
Both equations are satisfied, verifying that the solution is correct.
