Question

Solve the following simultaneous equations.
5x - 3y = 8; 3x + y = 2​

Answer 1

Given : -

• 5x - 3y = 8
• 3x + y = 2

To Find : -

• x = ?
• y = ?

Solution : -

5x - 3y = 8. . . (I)

3x + y = 2 . . . (II)

Let us write value of y in terms of x from equation (II) as

$\implies$ y = 2 - 3x . . . (III)

Substituting this value of y in equation (I).

$\implies$ 5x - 3y = 8

$\implies$ 5x - 3(2 - 3x) = 8

$\implies$ 5x - 6 + 9x = 8

$\implies$ 14x - 6 = 8

$\implies$ 14x = 8 + 6

$\implies$ 14x = 14

$\implies$ x = 1

Substituting x = 1 in equation (III).

$\implies$ y = 2 - 3x

$\implies$ y = 2 - 3 x 1

$\implies$ y = 2 - 3

$\implies$ y = -1

$\implies$ x = 1, y = -1 is the solution.

Answer 2

Given equations

$5x-3y=8--(1) \\3x+y=2--(2)$

Multiplying the second equation by 3, we get,

$9x+3y=6--(3)$

Solving (1) and (3), we get,

$5x-3y=8\\\underline {9x+3y=6}\\\underline{\underline{14x=14}}}}\\\implies x = 1$

Substituting the value of x in the second equation, we get,

$\implies 3(1)+y=2\\\implies 3+y=2\\\implies y = 2-3\\\implies y = -1$

$\boxed{\boxed{\bold{Therefore, \ the \ values \ of \ x \ and \ y \ are \ 1 \ and \ -1 \ respectively.}}}}}}}}$