Question

The points $(2,3)$ lies on the graph of the linear equation $3x-(a-1)y=2a-1.$ If the same point also liner the graph of the linear equation $5x+(1-2a)y=3b,$ then find the value of $b$

• A. $\frac{1}{4}$
• B. $-\frac{1}{4}$
• C. $-\frac{1}{3}$
• D. $\frac{1}{3}$

Answer 1

The correct option is D $\frac{1}{3}$

It is given that ($2,3$) lies on the graph of the linear equation $3x-(a-1)y=2a-1$

so, putting the value of $x=2,y=3$ we get

$3\times 2-(a-1)\times 3=2a-1\Rightarrow 6-3a+3=2a-1\Rightarrow -5a=-10\Rightarrow a=2$

again $(2,3)$ lies on the graph of the equation $5x+(1-2a)y=3b$

putting the value of $x=2,y=3,a=2$ we get,

$5\times 2+(1-2\times 2)\times 3=3b\Rightarrow 10+3-12=3b\Rightarrow 3b=1\Rightarrow b=\frac{1}{3}$