Question

The solution of the equations $5x+3y=16$ and $3x+5y=16$ is

• A. (2,3)
• B. (3,4)
• C. (2,2)
• D. (-3,0)

Answer 1

The correct option is C (2,2)

Given: $5x+3y=16$ …..(i)
and, $3x+5y=16$ …..(ii)
Multiplying (i) by 5, we get
$5(5x+3y)=5\times 16$
$\Rightarrow 25x+15y=80$ …..(iii)
Multiplying (ii) by 3, we get
$3(3x+5y)=3\times 16$
$\Rightarrow 9x+15y=48$ …..(iv)
Subtracting (iv) from (iii), we get '
$(25x+15y)–(9x+15y)=80–48$
$\Rightarrow 16x=32$
$\Rightarrow x=2$
Substituting x = 2 in (i), we get
$5\left(2\right)+3y=16$
$\Rightarrow 3y=16-10=6$
$\Rightarrow y=\frac{6}{3}=2$
Thus, (2, 2) is the solution for (i) and (ii).
Hence, the correct answer is option (c).