Question

If x=a. y -b is the solution of the equations x + y = 5 and 2x + 3y = 4. then the values of a
and b are respectively
(a) 6.-1
(b) 2,3
(c) 1,4
(d) 19/5, 6/5​

Answer 1

Correct Question :

If x=a, y=b is the solution of the equations x + y = 5 and 2x - 3y = 4, then the value of a and b are respectively

Answer:

a = 6/5

b = 19/5

Option (d)

Step-by-step explanation:

x = a. y = b is the solution of the equations x + y = 5 and 2x - 3y = 4

Put x = a and y = b,

➙ x + y = 5

➙ (a) + (b) = 5

➙ a + b = 5 ↬ [1]

➙ 2x + 3y = 4

➙ 2(a) - 3(b) = 4

➙ 2a - 3b = 4 ↬ [2]

Multiply equation [1] by 2,

➙ a + b = 5

➙ 2(a + b) = 2(5)

➙ 2a + 2b = 10 ↬ [3]

Subtract equation [2] from equation [3],

2a + 2b - (2a - 3b) = 10 - 4

2a + 2b - 2a + 3b = 6

  2b + 3b = 6

    5b = 6

     b = 6/5

Substitute b = 6/5 in equation [1],

a + b = 5

a + 6/5 = 5

 $\sf a=5-\dfrac{6}{5} \\\\ \sf a=\dfrac{5 \times 5}{5}-\dfrac{6}{5} \\\\ \sf a=\dfrac{25-6}{5} \\\\ \sf a=\dfrac{19}{5}$

Therefore,

the value of a is 19/5

the value of b is 6/5