Question

solve the pair of linear equations by only elimination method 2x+y=5
3x+2y=8​

Answer 1

Answer :- Here we have, 2x+y=5→(1)

Here we have, 2x+y=5→(1)3x+2y=8→(2)

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=10

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2 In the eq

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2 In the eq n

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2 In the eq n (1), put x=2,4+y=5

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2 In the eq n (1), put x=2,4+y=5So,

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2 In the eq n (1), put x=2,4+y=5So, x=1

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2 In the eq n (1), put x=2,4+y=5So, x=1

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2 In the eq n (1), put x=2,4+y=5So, x=1

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2 In the eq n (1), put x=2,4+y=5So, x=1 (x,y)=(2,1)

Here we have, 2x+y=5→(1)3x+2y=8→(2)Let Multiply eq n (1) by 2.So, 4x+2y=104x+2y=8________________x=2 In the eq n (1), put x=2,4+y=5So, x=1 (x,y)=(2,1)

Answer 2

Steps For Elimination Method

Step 1: Firstly, multiply both the given equations by some suitable non-zero constants to make the coefficients of any one of the variables (either x or y) numerically equal.

Step 2: After that, add or subtract one equation from the other in such a way that one variable gets eliminated. Now, if you get an equation in one variable, go to Step 3. Else;

If we obtain a true statement including no variable, then the original pair of equations has infinitely many solutions.

If we obtain a false statement including no variable, then the original pair of equations has no solution, i.e., it is inconsistent.

Step 3: Solve the equation in one variable (x or y) to get its value.

Step 4: Substitute this value in any of the given equations to get the value of another variable

Let us understand with a general case.

General Case: Taking a general case of two linear equations:

ax + by = c………(1)

px + qy = r……….(2)

Multiplying eq (1) by p, we get,

apx + bpy = cp ………..(3)

Similarly, on multiplying eq (2) with ‘a’, we get:

apx + aqy = ar………….(4)

As per the elimination method, the coefficient of x obtained in equation (3) and equation (4) is same.

In order to remove the variable x and get a linear equation in one variable, equation (4) is subtracted from equation (3). We get:

apx + bpy – apx – aqy = cp – ar

bpy – aqy = cp – ar

(bp – aq) y = cp – ar

y = (cp-ar)/(bp-aq)

Also, from equation (1) we get,

ax = c – by

Elimination Method to Solve Linear Equations in Two Variables