Question

# Solve Each system : Explain your choice of Solution method

2X - 3Y = 14

5X + 4Y = 12

Hint:

### Choose the correct method of solution and perform any arithmetic operation

and then find.

## The correct answer is: x=107/23 and y=(-36)/23

### Complete step by step solution:

We can use the method of elimination of the system of equations.

Let 2x -3y = 14…(i)

and 5x + 4y = 12….(ii)

On multiplying (i) with 5, we get 5(2x - 3y = 14)

⇒10x - 15y = 70…(iii)

On multiplying (ii) with 2, we get 2( 5x + 4y = 12)

⇒10x + 8y = 24…(iv)

Now, we have the coefficients of x in (iii) and (iv) to be the same.

On subtracting (iii) from (iv),

we get LHS to be 10x + 8y - (10x - 15y) = 8y + 15y = 23y

and RHS to be 24 - 70 = - 36

On equating LHS and RHS, we have 23y = - 36

On substituting the value of y in (i), we get

Hence we get

Note: We can also solve these system of equations by making the coefficients of y

to be the same in both the equations.

On multiplying (ii) with 2, we get 2( 5x + 4y = 12)

Now, we have the coefficients of x in (iii) and (iv) to be the same.

On subtracting (iii) from (iv),

we get LHS to be 10x + 8y - (10x - 15y) = 8y + 15y = 23y

and RHS to be 24 - 70 = - 36

On equating LHS and RHS, we have 23y = - 36

On substituting the value of y in (i), we get

Hence we get

Note: We can also solve these system of equations by making the coefficients of y

to be the same in both the equations.

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