Elimination Using Addition and Subtraction

In systems of equations where the coefficients of terms contain the same variable are opposites, the elimination method can be applied by adding the equations. If the coefficients of those terms are the similar, then the elimination method can be done by subtracting the equations. Let us some example problems for elimination using addition and subtraction.

Example Problems of Elimination Using Addition and Subtraction:

Example 1:

Solve: a-b=3 and 3a+b=1

Solution:

Step 1:  Here we are going to solve these equations.

Step 2: We need to add the two equations. Here the coefficients of the b terms,(-b+b)are opposite. So we can easily cancel the terms.

Step 3: When we simplify we get 4a=4.therefore a= 1.

Now we need to calculate the value of b.

Step 6: so, we plug in a value in any equation to find b.

Step 7: here the second equation is 3a+b=1.

Step 8: So,3(1)+b=1.Therefore b = -2

How to check the solution:

We know that a and b value now. So substitute a and b value in any equation. Let us take the first equation.

Step 1: a-b=3.The value of a is 1, and the value of b is -2.

Step 2: Therefore, 1- (-2)=3 .

Step 3: When we add both the sides, we get 3=3.

Suppose if we get a different answer on both the side, the answer must be wrong.



Example 2:

Solve: u+v=3 and –u+2v=6.

Solution:

Step 1:  Here we are going to solve these equations.

Step 2: We need to add the two equations. Here the coefficients of the b terms,(-u+u)are opposite. So we can easily cancel the terms.

Step 3: When we simplify we get 3v=9.therefore v= 3.

Now we need to calculate the value of u.

Step 6: so, we plug in v value in any equation to find u.

Step 7: here the first equation is u+v=3.

Step 8: So,u + 3 = 3.Therefore u = 0.



How to check the solution:

We know that a and b value now. So substitute a and b value in any equation. Let us take the first equation.

Step 1: u+v=3 The value of u is 0, and the value of v is 3.

Step 2: Therefore,0+3=3. 3 = 3

Step 3: When we add both the sides, we get 3=3.

Suppose if we get a different answer on both the side, the answer must be wrong.

These are the example problems of elimination using addition and subtraction.

Practise Problems of Elimination Using Addition and Subtraction:

1) X+y = 7 and x-y =9

2) 2s-r =12 and s+r = -27



Answer key :

1) X = 8 and y = -1

2) S = -22 and r = -5.