Question

Solve $11x+15y+23=0,7x-2y-20=0$ by elimination method

Answer 1

Elimination method: One or both the equations are multiplied by factors such that on addition or subtraction of the resulting two equations, only one variable remains

Solution:

Given that $11x+15y+23=0,7x-2y-20=0$

On multiplying first equation by $2$ and second equation by $15$, we get

$$\begin{gathered} 2\times [11x+15y+23]=0 \\ ⟹22x+30y+46=0\dots \dots \dots \dots \dots \left(1\right) \\ 15\times [7x-2y-20]=0 \\ ⟹105x-30y-300=0\dots \dots \dots \dots \left(2\right) \end{gathered}$$

adding both the equations, we get

$$\begin{gathered} 22x+30y+46+105x-30y-300=0 \\ 127x-254=0 \\ 127x=254 \\ x=\frac{254}{127} \\ ⟹x=2 \end{gathered}$$

Put the value of x in the equation$\left(1\right)$ we get

$$\begin{gathered} 22x+30y+46=0 \\ 22\left(2\right)+30y+46=0 \\ 44+30y+46=0 \\ 30y+90=0 \\ 30y=-90 \\ y=\frac{-90}{30} \\ y=-3 \end{gathered}$$

Hence, $x=2,y=-3$