In this page we are going to discuss about simultaneous equations concept. A set of independent equations in two or more variables is called a simultaneous equation. To find the value(s) of the variables for which the set of equation holds is called solving the equation. There are different methods used to solve simultaneous equations. In this article, we will learn how to solve the simultaneous equations by Substitution and Elimination methods with examples.
The general form of the simultaneous equation can be written as,
AX + BY = C,
DX + EY = F.
Elimination Method to solve simultaneous equations
Below mare the example on elimination method to solve simultaneous equations -
Examples:
Solve the simultaneous equations examples using Elimination method 4X + 5Y = 12, 3X - 5Y = 9.
Solution:
The given two equations are,
4X + 5Y = 12 -----------------(1)
3X - 5Y = 9 -----------------(2)
Step 1: Here the coefficient of one of the variables numerically equal and also opposite signs. So
Add the two equations for eliminating Y variable
Step 2: Add the like terms, (4X + 3X) + (5Y - 5Y) = 12 + 9.
Step 3: After the addition and elimination of Y, rewrite the equation as
7X = 21
Step 4: Divide 7 on both side of the equation
7X / 7 = 21 / 7
Step 5: After dividing, we get X = 3.
Step 6: Substitute the X value in the first equation
4(3) + 5Y = 12,
12 + 5Y = 12.
Step 7: Subtracting 12 both sides in the equation. We get Y value,
5Y = 12 - 12,
5Y = 0,
Y = 0.
Step 8: The solution for this equation is X = 3, Y = 0. Please express your views of this topic Decimal Multiplication by commenting on blog.
Substitution method to solving simultaneous equations
Below are the example on substitution method to solving simultaneous equations -
Examples:
Solve the simultaneous equations examples using substitution method Y= X + 2, X + Y = 4.
Solution:
Given, Y = X + 2 --------------(1)
X + Y = 4 --------------(2)
Step 1: Substitute the value of Y into the second equation. We get,
X + (X + 2) = 4
Step 2: Solve X
2X + 2 = 4 (subtract 2 both sides)
2X = 4 - 2
2X = 2, (divide 2 both sides)
X = 2/2,
X = 1.
Step 5: Substitute the value of X into the first equation.
Y = X + 2,
Y = 1 + 2,
Y = 3.
Step 7: The answer is X = 1 and Y = 3.
The general form of the simultaneous equation can be written as,
AX + BY = C,
DX + EY = F.
Elimination Method to solve simultaneous equations
Below mare the example on elimination method to solve simultaneous equations -
Examples:
Solve the simultaneous equations examples using Elimination method 4X + 5Y = 12, 3X - 5Y = 9.
Solution:
The given two equations are,
4X + 5Y = 12 -----------------(1)
3X - 5Y = 9 -----------------(2)
Step 1: Here the coefficient of one of the variables numerically equal and also opposite signs. So
Add the two equations for eliminating Y variable
Step 2: Add the like terms, (4X + 3X) + (5Y - 5Y) = 12 + 9.
Step 3: After the addition and elimination of Y, rewrite the equation as
7X = 21
Step 4: Divide 7 on both side of the equation
7X / 7 = 21 / 7
Step 5: After dividing, we get X = 3.
Step 6: Substitute the X value in the first equation
4(3) + 5Y = 12,
12 + 5Y = 12.
Step 7: Subtracting 12 both sides in the equation. We get Y value,
5Y = 12 - 12,
5Y = 0,
Y = 0.
Step 8: The solution for this equation is X = 3, Y = 0. Please express your views of this topic Decimal Multiplication by commenting on blog.
Substitution method to solving simultaneous equations
Below are the example on substitution method to solving simultaneous equations -
Examples:
Solve the simultaneous equations examples using substitution method Y= X + 2, X + Y = 4.
Solution:
Given, Y = X + 2 --------------(1)
X + Y = 4 --------------(2)
Step 1: Substitute the value of Y into the second equation. We get,
X + (X + 2) = 4
Step 2: Solve X
2X + 2 = 4 (subtract 2 both sides)
2X = 4 - 2
2X = 2, (divide 2 both sides)
X = 2/2,
X = 1.
Step 5: Substitute the value of X into the first equation.
Y = X + 2,
Y = 1 + 2,
Y = 3.
Step 7: The answer is X = 1 and Y = 3.
