Question

Test the whether the following system of equation has unique solution, infinite solution, or no solutions. If it has a unique solution then find the values ofx and y.
Test whether the following system of equations has a unique solution, infinite solu-
4x + 7y = 18
2x+y=4​

Answer 1

Answer:

(1,2)

Step-by-step explanation:

Given equations:

4x + 7y = 18

2x + y  = 4

Here, a₁ = 4,  b₁ = 7, c₁ = 18 and a₂ = 2, b₂ = 1, c₂ = 4

∴ a₁/a₂ = 4/2 = 2

and b₁/b₂ = 7/1 = 7

also, c₁/c₂ = 18/4 = 9/2

We can observe that a₁/a₂ ≠ b₁/b₂

∴ System of Equation has a unique solution.

Let 4x + 7y = 18  be  eqn-1

and 2x + y = 4  be  eqn2

​Multiply eqn2 by 2

∴ (2x + y = 4) × 2

= 4x + 2y = 8           {eqn 3}

Subtract eqn3 from eqn1

∴ 4x - 4x + 7y - 2y = 18 - 8

= 5y = 10

= y = 10/5

= y = 2

Put y = 2 in eqn 2

= 2x + 2 = 4

= 2x = 4 - 2

= x = 2/2

= x =1

∴ Solution of the system of equation = (1,2)

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