The general form of simultaneous linear equations is given as:
ax +by = c
dx + ey = f
1. Elimination Method: In the elimination method, we eliminate one of the variables from the equations by adding or subtracting the equations from each other. The aim is to get one of the variables to have the same coefficient in both equations so that we can add or subtract them easily.
Steps to solve simultaneous equations using the elimination method:
2. Substitution Method: In the substitution method, we solve one of the equations for one of the variables in terms of the other variable and then substitute that expression into the other equation.
Steps to solve simultaneous equations using the substitution method:
Example: Solve the following simultaneous equations using the elimination method.
4a + 5b = 12,
3a – 5b = 9
To solve the simultaneous equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. Here, we can eliminate b by adding the equations together because the coefficients of b are opposites:
4a + 5b = 12
3a – 5b = 9
7a = 21
Dividing both sides by 7, we get:
a = 3
Now, we can substitute the value of a into one of the equations and solve for b. Let's use the first equation:
4a + 5b = 12
4(3) + 5b = 12
12 + 5b = 12
5b = 0
b = 0
Therefore, the solution to the simultaneous equations is:
a = 3, b = 0.
Solving Simultaneous Linear Equations Using Substitution Method: Below is the solved example with steps to understand the solution of simultaneous linear equations using the substitution method in a better way.
Example: Solve the following simultaneous equations using the substitution method.
b= a + 2
a + b = 4.
Using the substitution method, we can substitute the first equation into the second equation:
b = a + 2
a + (a + 2) = 4
Simplifying the second equation:
2a + 2 = 4
2a = 2
a = 1
Now substituting the value of a in the first equation:
b = 1 + 2
b = 3
Therefore, the solution to the given simultaneous equations is a = 1 and b = 3.
406 videos217 docs164 tests


Explore Courses for Class 10 exam
