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Maths-

General

Easy

Question

Solve Each system : Explain your choice of Solution method
2X - 3Y = 14
5X + 4Y = 12

hint 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
$not stretchy rightwards double arrow y equals fraction numerator negative 36 over denominator 23 end fraction$
On substituting the value of y in (i), we get $2 x minus 3 cross times fraction numerator negative 36 over denominator 23 end fraction equals 14$
$not stretchy rightwards double arrow 2 x plus 108 over 23 equals 14$
   $not stretchy rightwards double arrow 2 x equals 14 minus 108 over 23$
   $not stretchy rightwards double arrow 2 x equals 214 over 23$
   $not stretchy rightwards double arrow x equals 107 over 23$
Hence we get $x equals 107 over 23 text and end text y equals fraction numerator negative 36 over denominator 23 end fraction$
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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