What kind of solutions does 3x + 2y = 4 and 2x - y = 5 have?

Solution:

Solving the linear equations simultaneously we have,

3x + 2y  =  4(1)

2x -   y   =  5(2)

Multiply equation (2) by 2 and add to equation (1)

3x  +  2y  =    4

4x  -   2y =    10

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7x  + 0    =    14

⇒ x  = 14/7 = 2

Substituting the obtained value of x = 2 in equation (1) we have 

3(2) + 2y  =  4

6  + 2y   =  4 

2y  = 4 - 6 

2y    = -2

y = -1

Hence the given set of equations are consistent and have a unique solution given by x = 2, and y = -1.

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What kind of solutions does 3x + 2y = 4 and 2x - y = 5 have?

Summary:

The equations 3x + 2y = 4 and 2x - y = 5 are consistent in nature and have a unique solution given by x = 2, and y = -1.