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Class 12

>>Applied Mathematics

>>Linear Equations

>>Solving a Pair of Linear Equations - Substitution Method

>>Solve the following sets of simultaneous

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Solve the following sets of simultaneous equations.

2x+y=5;3x−y=5

Medium

Solution

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Given

2x+y=5

y=5−2x

3x−y=5

substitute value of y from (1) in the above equation, we get

3x−(5−2x)=5

3x−5+2x=5

3x+2x=5+5

5x=10

x=

5

10

x=2

Putting value of x in (1) ,we get

y=5−2x

y=5−2×2

y=5−4

y=1

Given equations-

3x+y=15 -eq.1

2x-y=5 -eq.2

Adding eq.1 and eq.2, we get-

3x+y+2x-y=15+5

》5x=20

》 x=20/5

》 x=4

Substituting this value of x in eq.1-

3x+y=15

》3(4)+y=15

》12+y=15

》y=15-12

》y=3