Which type of solution will the pair of linear equation X + 3 Y is equal to 4 and 3 X + Y = 5 have?

Question

Answer

Type of Solution for the Pair of Linear Equations X + 3Y = 4 and 3X + Y = 5

Introduction

When two linear equations are given, they can have three types of solutions- unique solution, no solution, and infinite solutions. The type of solution depends on the coefficients and constants of the equations.

Analysis of the Equations

The given pair of linear equations are:

X + 3Y = 4

3X + Y = 5

To determine the type of solution for this pair of linear equations, we can use the elimination method. In this method, we add or subtract the equations to eliminate one of the variables.

Elimination Method

To eliminate Y, we can multiply the first equation by 3 and the second equation by -1.

3(X + 3Y) = 12

-1(3X + Y) = -5

On simplification, we get:

3X + 9Y = 12

-3X - Y = -5

Adding both equations, we get:

8Y = 7

Y = 7/8

Substitution Method

Now that we have found the value of Y, we can substitute it in either of the equations to find the value of X.

Using the first equation, we get:

X + 3(7/8) = 4

X + 21/8 = 32/8

X = 11/8

Conclusion

Therefore, the pair of linear equations X + 3Y = 4 and 3X + Y = 5 has a unique solution, which is X = 11/8 and Y = 7/8.

Answer

X+3y=43x+y=5a1/a2=1/3.  and b1/b2=3/1as they are not equal, so the pair of equations will have a unique solution.

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