Question

Solve the equation 2x+3y=9and y-x=-2

Answer 1

Given two equations are,

$2x+3y=9$-----------(1)

$y-x=-2$-----------(2)

Multiply equation (2) with $2$

$2(y-x)=2(-2)$

$2y-2x=-4$--------(3)

Add equation (1) and (3)

$2x+3y+2y-2x=9+(-4)\\ 5y=5\\ y=1$

Substitute $y=1$ in equation (1)

$2x+3(1)=9\\2x+3=9\\2x=9-3\\2x=6\\x=3$

Therefore, the value of $x$ is $3$ and value of $y$ is $1$.

Answer 2

Given,

$2x+3y=9$_____(1)

$y-x=-2$______(2)

Multiply equation (2) with 3

$3y-3x=-6$_____(3)

Subtract equation (1)from equation (3)

$3y-3x-(2x+3y)=-6-9$

$-5x=-15$

$x= 3$

Substitute $x=3$ in equation (3)

$3y-3\times3=-6$

$3y=-6+9\\3y=3\\y=1$

Therefore, the values of $x$ and $y$ is $3,1$.